Pythagorean theorem proof using similarity

WEBVTT
Kind: captions
Language: en

00:00:00.670 --> 00:00:04.045
This triangle that we have right
over here is a right triangle.

00:00:04.045 --> 00:00:06.600
And it's a right triangle
because it has a 90 degree

00:00:06.600 --> 00:00:09.240
angle, or has a
right angle in it.

00:00:09.240 --> 00:00:12.520
Now, we call the longest
side of a right triangle,

00:00:12.520 --> 00:00:14.599
we call that side,
and you could either

00:00:14.599 --> 00:00:17.140
view it as the longest side of
the right triangle or the side

00:00:17.140 --> 00:00:20.980
opposite the 90 degree angle,
it is called a hypotenuse.

00:00:20.980 --> 00:00:23.740
It's a very fancy word
for a fairly simple idea,

00:00:23.740 --> 00:00:26.140
just the longest side of a
right triangle or the side

00:00:26.140 --> 00:00:27.542
opposite the 90 degree angle.

00:00:27.542 --> 00:00:29.500
And it's just good to
know that because someone

00:00:29.500 --> 00:00:30.090
might say hypotenuse.

00:00:30.090 --> 00:00:32.548
You're like, oh, they're just
talking about this side right

00:00:32.548 --> 00:00:36.580
here, the side longest, the side
opposite the 90 degree angle.

00:00:36.580 --> 00:00:38.860
Now, what I want
to do in this video

00:00:38.860 --> 00:00:42.167
is prove a relationship, a
very famous relationship.

00:00:42.167 --> 00:00:43.750
And you might see
where this is going.

00:00:43.750 --> 00:00:46.370
A very famous relationship
between the lengths

00:00:46.370 --> 00:00:48.840
of the sides of
a right triangle.

00:00:48.840 --> 00:00:53.210
So let's say that the length of
AC, so uppercase A, uppercase

00:00:53.210 --> 00:00:55.930
C, let's call that
length lowercase a.

00:00:55.930 --> 00:01:00.040
Let's call the length of BC
lowercase b right over here.

00:01:00.040 --> 00:01:03.420
I'll use uppercases for
points, lowercases for lengths.

00:01:03.420 --> 00:01:06.630
And let's call the length of the
hypotenuse, the length of AB,

00:01:06.630 --> 00:01:07.822
let's call that c.

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And let's see if we can come
up with the relationship

00:01:10.030 --> 00:01:12.790
between a, b, and c.

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And to do that I'm
first going to construct

00:01:14.780 --> 00:01:16.410
another line or
another segment, I

00:01:16.410 --> 00:01:19.520
should say, between
c and the hypotenuse.

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And I'm going to
construct it so that they

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intersect at a right angle.

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And you can always do that.

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And we'll call this point
right over here we'll.

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Call this point capital D.

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And if you're wondering,
how can you always do that?

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You could imagine rotating
this entire triangle like this.

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This isn't a rigorous proof,
but it just kind of gives you

00:01:36.050 --> 00:01:38.100
the general idea of
how you can always

00:01:38.100 --> 00:01:39.810
construct a point like this.

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So if I've rotated it around.

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So now our hypotenuse, we're
now sitting on our hypotenuse.

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This is now point
B, this is point A.

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So we've rotated the whole
thing all the way around.

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This is point C. You
could imagine just

00:01:52.710 --> 00:01:55.820
dropping a rock from point C,
maybe with a string attached,

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and it would hit the
hypotenuse at a right angle.

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So that's all we did here to
establish segment CD into where

00:02:02.980 --> 00:02:05.570
we put our point D
right over there.

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And the reason why
did that is now we

00:02:07.220 --> 00:02:09.289
can do all sorts of
interesting relationships

00:02:09.289 --> 00:02:10.490
between similar triangles.

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Because we have
three triangles here.

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We have triangle ADC,
we have triangle DBC,

00:02:15.604 --> 00:02:17.520
and then we have the
larger original triangle.

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And we can hopefully
establish similarity

00:02:19.890 --> 00:02:21.980
between those triangles.

00:02:21.980 --> 00:02:27.590
And first I'll show you that ADC
is similar to the larger one.

00:02:27.590 --> 00:02:29.710
Because both of them
have a right angle.

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ADC has a right angle
right over here.

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Clearly if this
angle is 90 degrees,

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then this angle is going
to be 90 degrees as well.

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They are supplementary.

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They have to add up to 180.

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And so they both have
a right angle in them.

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So the smaller one
has a right angle.

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The larger one clearly
has a right angle.

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That's where we started from.

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And they also both
share this angle right

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over here, angle
DAC or BAC, however

00:02:52.150 --> 00:02:53.580
you want to refer to it.

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So we can actually write
down that triangle.

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I'm going to start with
the smaller one, ADC.

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And maybe I'll shade
it in right over here.

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So this is the triangle
we're talking about.

00:03:04.023 --> 00:03:05.429
Triangle ADC.

00:03:05.429 --> 00:03:07.470
And I went from the blue
angle to the right angle

00:03:07.470 --> 00:03:10.620
to the unlabeled angle from the
point of view of triangle ADC.

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This right angle isn't applying
to that right over there.

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It's applying to
the larger triangle.

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So we could say triangle
ADC is similar to triangle--

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once again, you want to
start at the blue angle.

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A. Then we went to
the right angle.

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So we have to go to
the right angle again.

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So it's ACB.

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And because they're
similar, we can set up

00:03:39.270 --> 00:03:42.220
a relationship between
the ratios of their sides.

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For example, we know the
ratio of corresponding sides

00:03:44.705 --> 00:03:47.080
are going to do, well, in
general for a similar triangle,

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we know the ratio of
the corresponding sides

00:03:48.640 --> 00:03:49.890
are going to be a constant.

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So we could take the ratio of
the hypotenuse of the smaller

00:03:54.100 --> 00:03:54.960
triangle.

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So the hypotenuse is AC.

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So AC over the hypotenuse
over the larger one, which

00:04:00.710 --> 00:04:10.480
is a AB, AC over AB is going
to be the same thing as AD

00:04:10.480 --> 00:04:14.180
as one of the legs, AD.

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And just to show that, I'm just
taking corresponding points

00:04:16.959 --> 00:04:23.794
on both similar triangles,
this is AD over AC.

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You could look at these
triangles yourself and show,

00:04:25.960 --> 00:04:29.930
look, AD, point AD, is
between the blue angle

00:04:29.930 --> 00:04:31.410
and the right angle.

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Sorry, side AD is between the
blue angle and the right angle.

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Side AC is between the blue
angle and the right angle

00:04:38.025 --> 00:04:39.010
on the larger triangle.

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So both of these are
from the larger triangle.

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These are the corresponding
sides on the smaller triangle.

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And if that is confusing
looking at them visually,

00:04:46.990 --> 00:04:50.199
as long as we wrote our
similarity statement correctly,

00:04:50.199 --> 00:04:51.990
you can just find the
corresponding points.

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AC corresponds to AB
on the larger triangle,

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AD on the smaller
triangle corresponds

00:04:58.840 --> 00:05:02.330
to AC on the larger triangle.

00:05:02.330 --> 00:05:06.920
And we know that AC, we can
rewrite that as lowercase a.

00:05:06.920 --> 00:05:10.860
AC is lowercase a.

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We don't have any
label for AD or for AB.

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Sorry, we do have
a label for AB.

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That is c right over here.

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We don't have a label for AD.

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So AD, let's just
call that lowercase d.

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So lowercase d applies to
that part right over there.

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c applies to that entire
part right over there.

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And then we'll call DB,
let's call that length e.

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That'll just make things a
little bit simpler for us.

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So AD we'll just call d.

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And so we have a over
c is equal to d over a.

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If we cross multiply, you have
a times a, which is a squared,

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is equal to c times
d, which is cd.

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So that's a little bit
of an interesting result.

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Let's see what we can do
with the other triangle

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right over here.

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So this triangle
right over here.

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So once again, it
has a right angle.

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The larger one
has a right angle.

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And they both share this
angle right over here.

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So by angle, angle
similarity, the two triangles

00:06:07.070 --> 00:06:08.210
are going to be similar.

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So we could say triangle
BDC, we went from pink

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to right to not labeled.

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So triangle BDC is
similar to triangle.

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Now we're going to look
at the larger triangle,

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we're going to start
at the pink angle.

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B. Now we're going to
go to the right angle.

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CA.

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BCA.

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From pink angle to right
angle to non-labeled angle,

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at least from the
point of view here.

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We labeled it before
with that blue.

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So now let's set up some
type of relationship here.

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We can say that the ratio on
the smaller triangle, BC, side

00:06:45.040 --> 00:06:50.130
BC over BA, BC over
BA, once again,

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we're taking the
hypotenuses of both of them.

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So BC over BA is going
to be equal to BD.

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Let me do this in another color.

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BD.

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So this is one of the legs.

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BD.

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The way I drew it
is the shorter legs.

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BD over BC.

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I'm just taking the
corresponding vertices.

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Over BC.

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And once again, we know BC is
the same thing as lowercase b.

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BC is lowercase b.

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BA is lowercase c.

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And then BD we defined
as lowercase e.

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So this is lowercase e.

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We can cross
multiply here and we

00:07:33.210 --> 00:07:37.830
get b times b, which, and I've
mentioned this in many videos,

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cross multiplying is really
the same thing as multiplying

00:07:40.310 --> 00:07:42.680
both sides by both denominators.

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b times b is b squared
is equal to ce.

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And now we can do something
kind of interesting.

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We can add these two statements.

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Let me rewrite the
statement down here.

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So b squared is equal to ce.

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So if we add the
left hand sides,

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we get a squared plus b squared.

00:08:02.120 --> 00:08:09.420
a squared plus b squared
is equal to cd plus ce.

00:08:12.595 --> 00:08:14.917
And then we have a c
both of these terms,

00:08:14.917 --> 00:08:16.000
so we could factor it out.

00:08:16.000 --> 00:08:19.880
So this is going to be equal
to-- we can factor out the c.

00:08:19.880 --> 00:08:22.952
It's going to be equal
to c times d plus e.

00:08:22.952 --> 00:08:29.790
c times d plus e and
close the parentheses.

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Now what is d plus e?

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d is this length,
e is this length.

00:08:34.159 --> 00:08:37.169
So d plus e is actually
going to be c as well.

00:08:37.169 --> 00:08:38.496
So this is going to be c.

00:08:38.496 --> 00:08:41.039
So you have c times c,
which is just the same thing

00:08:41.039 --> 00:08:43.030
as c squared.

00:08:43.030 --> 00:08:45.700
So now we have an
interesting relationship.

00:08:45.700 --> 00:08:51.150
We have that a squared plus b
squared is equal to c squared.

00:08:51.150 --> 00:08:52.580
Let me rewrite that.

00:08:52.580 --> 00:08:54.300
a squared.

00:08:54.300 --> 00:08:58.623
Well, let me just do
an arbitrary new color.

00:08:58.623 --> 00:09:02.380
I deleted that by accident,
so let me rewrite it.

00:09:02.380 --> 00:09:07.390
So we've just established
that a squared plus b squared

00:09:07.390 --> 00:09:09.400
is equal to c squared.

00:09:09.400 --> 00:09:11.320
And this is just an
arbitrary right triangle.

00:09:11.320 --> 00:09:13.590
This is true for any
two right triangles.

00:09:13.590 --> 00:09:17.120
We've just established that
the sum of the squares of each

00:09:17.120 --> 00:09:20.060
of the legs is equal to the
square of the hypotenuse.

00:09:20.060 --> 00:09:22.550
And this is probably
what's easily

00:09:22.550 --> 00:09:26.220
one of the most famous
theorem in mathematics, named

00:09:26.220 --> 00:09:27.360
for Pythagoras.

00:09:27.360 --> 00:09:30.370
Not clear if he's the first
person to establish this,

00:09:30.370 --> 00:09:32.310
but it's called the
Pythagorean Theorem.

00:09:38.290 --> 00:09:41.469
And it's really the basis of,
well, all not all of geometry,

00:09:41.469 --> 00:09:43.510
but a lot of the geometry
that we're going to do.

00:09:43.510 --> 00:09:45.880
And it forms the basis of a
lot of the trigonometry we're

00:09:45.880 --> 00:09:46.230
going to do.

00:09:46.230 --> 00:09:47.550
And it's a really
useful way, if you

00:09:47.550 --> 00:09:49.299
know two of the sides
of a right triangle,

00:09:49.299 --> 00:09:51.890
you can always find the third.


Finding area using similarity and congruence

WEBVTT
Kind: captions
Language: en

00:00:00.810 --> 00:00:02.300
So in this problem
here, we're told

00:00:02.300 --> 00:00:05.350
that the triangle
ACE is isosceles.

00:00:05.350 --> 00:00:07.340
So that's this big
triangle right here.

00:00:07.340 --> 00:00:10.660
It's isosceles, which means
it has two equal sides,

00:00:10.660 --> 00:00:12.590
and we also know from
isosceles triangles

00:00:12.590 --> 00:00:15.250
that the base angles
must be equal.

00:00:15.250 --> 00:00:17.590
So these two base angles
are going to be equal.

00:00:17.590 --> 00:00:20.740
And this side right over here
is going to be equal in length

00:00:20.740 --> 00:00:21.920
to this side over here.

00:00:21.920 --> 00:00:24.790
We could say AC is
going to be equal to CE,

00:00:24.790 --> 00:00:27.590
so we get all of that
from this first statement

00:00:27.590 --> 00:00:29.090
right over there.

00:00:29.090 --> 00:00:31.400
Then they give us some
more clues, or some more

00:00:31.400 --> 00:00:32.030
information.

00:00:32.030 --> 00:00:34.120
They say CG is equal to 24.

00:00:34.120 --> 00:00:35.960
So this is CG right over here.

00:00:35.960 --> 00:00:38.020
It has length 24.

00:00:38.020 --> 00:00:43.410
They tell us BH is equal
to DF, so those two things

00:00:43.410 --> 00:00:45.010
are going to be congruent.

00:00:45.010 --> 00:00:46.640
They're going to
be the same length.

00:00:46.640 --> 00:00:50.700
Then they tell us that
GF is equal to 12.

00:00:50.700 --> 00:00:52.610
So this is GF right over here.

00:00:52.610 --> 00:00:55.210
So GF is equal to 12.

00:00:55.210 --> 00:00:57.360
That's that distance
right over there.

00:00:57.360 --> 00:01:00.910
And then finally, they tell
us that FE is equal to 6.

00:01:00.910 --> 00:01:04.330
So this is FE, and
then finally, they

00:01:04.330 --> 00:01:06.706
ask us, what is
the area of CBHFD?

00:01:14.420 --> 00:01:18.130
They're asking us for the area
of this part right over here.

00:01:18.130 --> 00:01:20.770
That part and that
part right over there.

00:01:20.770 --> 00:01:21.465
That is CBHFD.

00:01:23.604 --> 00:01:25.270
So let's think about
how we can do this.

00:01:25.270 --> 00:01:27.870
So we could figure out the
area of the larger triangle,

00:01:27.870 --> 00:01:29.410
and then from that
we could subtract

00:01:29.410 --> 00:01:31.900
the areas of these
little pieces at the end.

00:01:31.900 --> 00:01:34.510
Then, we'll be able to figure
out this middle area, this area

00:01:34.510 --> 00:01:35.260
that I've shaded.

00:01:35.260 --> 00:01:38.830
And we don't have all the
information yet to solve that.

00:01:38.830 --> 00:01:41.880
We know what the height, or the
altitude, of this triangle is,

00:01:41.880 --> 00:01:43.005
but we don't know its base.

00:01:43.005 --> 00:01:44.671
If we knew its base,
then we'd say, hey,

00:01:44.671 --> 00:01:45.612
1/2 base times height.

00:01:45.612 --> 00:01:47.070
We'd get the area
of this triangle,

00:01:47.070 --> 00:01:49.060
and then we'd have to
subtract out these areas.

00:01:49.060 --> 00:01:50.934
We don't have full
information there, either.

00:01:50.934 --> 00:01:52.260
We don't know this height.

00:01:52.260 --> 00:01:53.290
Once we know that
height, then we

00:01:53.290 --> 00:01:55.730
could figure out this height,
but we also don't quite yet

00:01:55.730 --> 00:01:58.220
know what this length
right over here is.

00:01:58.220 --> 00:02:00.590
So let's just take
it piece by piece.

00:02:00.590 --> 00:02:03.310
So the first thing we might
want to do, and you might guess,

00:02:03.310 --> 00:02:05.393
because we've been talking
a lot about similarity,

00:02:05.393 --> 00:02:07.760
is making some type of
argument about similarity

00:02:07.760 --> 00:02:10.169
here, because there's a
bunch of similar triangles.

00:02:10.169 --> 00:02:17.810
For example, triangle CGE shares
this angle with triangle DFE.

00:02:17.810 --> 00:02:20.510
They both share this
orange angle right here,

00:02:20.510 --> 00:02:23.960
and they both have this
right angle right over here.

00:02:23.960 --> 00:02:25.600
So they have two
angles in common.

00:02:25.600 --> 00:02:27.840
They're going to be
similar by angle-angle.

00:02:27.840 --> 00:02:28.700
And you can actually
show that there's

00:02:28.700 --> 00:02:30.200
going to be a third
angle in common,

00:02:30.200 --> 00:02:32.260
because these two
are parallel lines.

00:02:32.260 --> 00:02:47.150
So we can write that triangle
CGE is similar to triangle DFE,

00:02:47.150 --> 00:02:49.510
and we know that by angle-angle.

00:02:49.510 --> 00:02:52.290
We have one set of
corresponding angles congruent,

00:02:52.290 --> 00:02:54.710
and then this angle
is in both triangles,

00:02:54.710 --> 00:02:57.380
so it is a set of
corresponding congruent angles

00:02:57.380 --> 00:02:58.750
right over there.

00:02:58.750 --> 00:03:00.750
And so then, once we know
that they are similar,

00:03:00.750 --> 00:03:02.660
we can set up the
ratio between sides,

00:03:02.660 --> 00:03:05.300
because we have some information
about some of the sides.

00:03:05.300 --> 00:03:09.524
So we know that the ratio
between DF and this side

00:03:09.524 --> 00:03:11.940
right over here, which is a
corresponding side-- the ratio

00:03:11.940 --> 00:03:19.110
between DF and CG,
which is 24, is

00:03:19.110 --> 00:03:24.030
going to be the same thing as
the ratio between FE, which

00:03:24.030 --> 00:03:28.210
is 6, and GE, which is not 12.

00:03:28.210 --> 00:03:29.600
It's 12 plus 6.

00:03:29.600 --> 00:03:31.437
It is 18.

00:03:31.437 --> 00:03:32.270
And then, let's see.

00:03:32.270 --> 00:03:34.940
6 over 18, this
is just 1 over 3.

00:03:34.940 --> 00:03:42.620
You get 3DF is equal to 24.

00:03:42.620 --> 00:03:45.620
I just cross-multiplied, or
you could multiply both sides

00:03:45.620 --> 00:03:48.089
by 24, multiply both sides by 3.

00:03:48.089 --> 00:03:48.880
You would get this.

00:03:48.880 --> 00:03:51.130
Actually, you could just
multiply both sides times 24,

00:03:51.130 --> 00:03:53.550
and you'll get 24 times 1/3.

00:03:53.550 --> 00:03:55.030
But we'll just do it this way.

00:03:55.030 --> 00:03:56.240
Divide both sides by 3.

00:03:56.240 --> 00:04:00.300
You get DF is equal to 8.

00:04:00.300 --> 00:04:03.760
So we found out that DF is
equal to 8, that length right

00:04:03.760 --> 00:04:04.720
over there.

00:04:04.720 --> 00:04:06.450
And that's useful
for us because we

00:04:06.450 --> 00:04:13.140
know that this length right
over here is also equal to 8.

00:04:13.140 --> 00:04:14.760
And now what can we do?

00:04:14.760 --> 00:04:18.290
Well, it seems like we could
make another similarity

00:04:18.290 --> 00:04:20.800
argument, because we have
this angle right over here.

00:04:20.800 --> 00:04:23.860
It is congruent to that
angle right over there,

00:04:23.860 --> 00:04:25.940
and we also have
this angle, which

00:04:25.940 --> 00:04:27.140
is going to be 90 degrees.

00:04:27.140 --> 00:04:28.870
We have a 90-degree angle there.

00:04:28.870 --> 00:04:30.920
And actually, that
by itself is actually

00:04:30.920 --> 00:04:33.350
enough to say that we have
two similar triangles.

00:04:33.350 --> 00:04:34.850
We don't even have
to show that they

00:04:34.850 --> 00:04:36.190
have a congruent side here.

00:04:36.190 --> 00:04:38.565
And actually, we're going to
show that these are actually

00:04:38.565 --> 00:04:41.220
congruent triangles that we're
dealing with right over here.

00:04:41.220 --> 00:04:43.299
So we have two angles,
and actually, we

00:04:43.299 --> 00:04:44.590
could just go straight to that.

00:04:44.590 --> 00:04:46.620
Because when we talk
about congruency,

00:04:46.620 --> 00:04:49.071
if you have an angle that's
congruent to another angle,

00:04:49.071 --> 00:04:51.070
another angle that's
congruent to another angle,

00:04:51.070 --> 00:04:53.370
and then a side that's
congruent to another side,

00:04:53.370 --> 00:04:55.810
you are dealing with
two congruent triangles.

00:04:55.810 --> 00:05:00.140
So we can write-- let
me write it over here.

00:05:00.140 --> 00:05:01.700
I'll write it in pink.

00:05:01.700 --> 00:05:08.400
Triangle AHB is
congruent to-- you

00:05:08.400 --> 00:05:10.220
want to get the
corresponding vertices

00:05:10.220 --> 00:05:12.302
right-- is congruent
to triangle EFD.

00:05:17.870 --> 00:05:23.710
And we know that, because we
have angle-angle-side postulate

00:05:23.710 --> 00:05:25.320
for congruency.

00:05:25.320 --> 00:05:27.102
And if the two
triangles are congruent,

00:05:27.102 --> 00:05:28.310
that makes things convenient.

00:05:28.310 --> 00:05:30.736
That means if this side
is 8, that side is 8.

00:05:30.736 --> 00:05:31.610
We already knew that.

00:05:31.610 --> 00:05:33.318
That's how we established
our congruency.

00:05:33.318 --> 00:05:35.497
But that means if this
side has length 6,

00:05:35.497 --> 00:05:37.330
then the corresponding
side of this triangle

00:05:37.330 --> 00:05:40.060
is also going to have length 6.

00:05:40.060 --> 00:05:43.080
So we can write this
length right over here

00:05:43.080 --> 00:05:45.480
is also going to be 6.

00:05:45.480 --> 00:05:48.510
I can imagine you can imagine
where all this is going to go,

00:05:48.510 --> 00:05:50.090
but we want to
prove to ourselves.

00:05:50.090 --> 00:05:52.294
We want to know for
sure what the area is.

00:05:52.294 --> 00:05:54.960
We don't want to say, hey, maybe
this is the same thing as that.

00:05:54.960 --> 00:05:56.735
Let's just actually
prove it to ourselves.

00:05:56.735 --> 00:05:57.860
So how do we figure it out?

00:05:57.860 --> 00:06:00.276
We've almost figured out the
entire base of this triangle,

00:06:00.276 --> 00:06:03.020
but we still haven't figured
out the length of HG.

00:06:03.020 --> 00:06:05.300
Well, now we can use a
similarity argument again,

00:06:05.300 --> 00:06:08.470
because we can see that
triangle ABH is actually

00:06:08.470 --> 00:06:11.440
similar to triangle ACG.

00:06:11.440 --> 00:06:13.630
They both have this
angle here, and then

00:06:13.630 --> 00:06:16.300
they both have a right angle.

00:06:16.300 --> 00:06:18.230
ABH has a right angle there.

00:06:18.230 --> 00:06:20.130
ACG has a right angle
right over there.

00:06:20.130 --> 00:06:21.260
So you have two angles.

00:06:21.260 --> 00:06:24.470
Two corresponding angles
are equal to each other.

00:06:24.470 --> 00:06:26.730
You're now dealing
with similar triangles.

00:06:26.730 --> 00:06:33.770
So we know that triangle
ABH-- I'll just write it

00:06:33.770 --> 00:06:35.790
as AHB, since I already
wrote it this way.

00:06:35.790 --> 00:06:41.111
AHB is similar to triangle AGC.

00:06:41.111 --> 00:06:42.860
You want to make sure
you get the vertices

00:06:42.860 --> 00:06:43.651
in the right order.

00:06:43.651 --> 00:06:44.700
A is the orange angle.

00:06:44.700 --> 00:06:48.140
G is the right angle, and
then C is the unlabeled angle.

00:06:48.140 --> 00:06:51.613
This is similar to triangle AGC.

00:06:55.502 --> 00:06:56.960
And what that does
for us is now we

00:06:56.960 --> 00:07:00.910
can use the ratios to figure
out what HG is equal to.

00:07:00.910 --> 00:07:02.640
So what could we say over here?

00:07:02.640 --> 00:07:04.850
Well, we could say
that 8 over 24--

00:07:04.850 --> 00:07:07.950
BH over its corresponding
side of the larger triangle--

00:07:07.950 --> 00:07:17.856
so we say 8 over 24 is equal to
6 over not HG, but over a AG.

00:07:17.856 --> 00:07:21.700
6 over AG, and I think you
can see where this is going.

00:07:21.700 --> 00:07:23.410
You have 1/3.

00:07:23.410 --> 00:07:29.280
1/3 is equal to 6 over AG, or
we can cross-multiply here,

00:07:29.280 --> 00:07:34.450
and we can get AG
is equal to 18.

00:07:34.450 --> 00:07:37.150
So this entire length
right over here is 18.

00:07:37.150 --> 00:07:41.224
If AG is 18 and AH
is 6, then HG is 12.

00:07:41.224 --> 00:07:43.390
This is what you might have
guessed if you were just

00:07:43.390 --> 00:07:45.181
trying to guess the
answer right over here.

00:07:45.181 --> 00:07:47.100
But now we have
proven to ourselves

00:07:47.100 --> 00:07:51.180
that this base has length
of-- well, we have 18 here,

00:07:51.180 --> 00:07:52.910
and then we have
another 18 here.

00:07:52.910 --> 00:07:55.890
So it has a length of 36.

00:07:55.890 --> 00:07:59.410
So the entire base here is 36.

00:07:59.410 --> 00:08:01.099
So that is 36.

00:08:01.099 --> 00:08:02.640
And so now we can
figure out the area

00:08:02.640 --> 00:08:06.080
of the entire
isosceles triangle.

00:08:06.080 --> 00:08:10.590
So the area of
ACE is going to be

00:08:10.590 --> 00:08:18.010
equal to 1/2 times the
base, which is 36, times 24.

00:08:18.010 --> 00:08:23.780
And so this is going to be
the same thing as 1/2 times 36

00:08:23.780 --> 00:08:25.566
is 18.

00:08:25.566 --> 00:08:27.440
18 times 24.

00:08:27.440 --> 00:08:29.660
I'll just do that
over here on the top.

00:08:29.660 --> 00:08:33.360
So 18 times 24.

00:08:33.360 --> 00:08:35.950
8 times 4 is 32.

00:08:35.950 --> 00:08:39.564
1 times 4 is 4, plus 3 is 7.

00:08:39.564 --> 00:08:41.230
Then we put as 0 here,
because we're now

00:08:41.230 --> 00:08:43.309
dealing not with 2, but 20.

00:08:43.309 --> 00:08:46.860
You have 2 times 8 is 16.

00:08:46.860 --> 00:08:48.400
2 times 1 is 2, plus 1.

00:08:48.400 --> 00:08:54.060
So it's 360, and then you
have a 2, 7 plus 6 is 13.

00:08:54.060 --> 00:08:56.270
1 plus 3 is 4.

00:08:56.270 --> 00:09:00.480
So the area of ACE
is equal to 432.

00:09:00.480 --> 00:09:01.840
But we're not done yet.

00:09:01.840 --> 00:09:04.730
This area that we
care about is the area

00:09:04.730 --> 00:09:09.040
of the entire triangle
minus this area

00:09:09.040 --> 00:09:11.950
and minus this area
right over here.

00:09:11.950 --> 00:09:15.390
So what is the area of
each of these little wedges

00:09:15.390 --> 00:09:16.140
right over here?

00:09:16.140 --> 00:09:19.210
So it's going to be
1/2 times 8 times 6.

00:09:19.210 --> 00:09:22.000
So 1/2 times 8 is 4 times 6.

00:09:22.000 --> 00:09:24.900
So this is going to be
24 right over there,

00:09:24.900 --> 00:09:27.570
and this is going to be
another 24 right over there.

00:09:27.570 --> 00:09:32.250
So this is going to be equal
to 432 minus 24 minus 24,

00:09:32.250 --> 00:09:35.985
or minus 48, which
is equal to-- and we

00:09:35.985 --> 00:09:37.360
could try to do
this in our head.

00:09:37.360 --> 00:09:40.740
If we subtract 32, we're
going to get to 400.

00:09:40.740 --> 00:09:44.230
And then we're going to
have to subtract another 16.

00:09:44.230 --> 00:09:45.790
So if you subtract
10 from 400, you

00:09:45.790 --> 00:09:51.802
get to 390, so that you get to
384-- whatever the units were.

00:09:51.802 --> 00:09:54.260
If these were in meters, then
this would be meters squared.

00:09:54.260 --> 00:09:56.790
If this was centimeters, this
would be centimeters squared.

00:09:56.790 --> 00:09:57.750
Did I do that right?

00:09:57.750 --> 00:09:59.720
Let me go the other way.

00:09:59.720 --> 00:10:04.320
If I add 40 to this, 24 plus
another 8 gets me to 432.

00:10:04.320 --> 00:10:06.259
Yup, we're done.


Similar triangle example problems

WEBVTT
Kind: captions
Language: en

00:00:00.574 --> 00:00:01.990
What I want to do
in this video is

00:00:01.990 --> 00:00:04.771
see if we can identify similar
triangles here and prove

00:00:04.771 --> 00:00:06.520
to ourselves that they
really are similar,

00:00:06.520 --> 00:00:09.080
using some of the postulates
that we've set up.

00:00:09.080 --> 00:00:10.930
So over here, I
have triangle BDC.

00:00:10.930 --> 00:00:13.870
It's inside of triangle AEC.

00:00:13.870 --> 00:00:16.010
They both share this
angle right over there,

00:00:16.010 --> 00:00:17.140
so that gives us one angle.

00:00:17.140 --> 00:00:19.020
We need two to get
to angle-angle,

00:00:19.020 --> 00:00:20.980
which gives us similarity.

00:00:20.980 --> 00:00:22.990
And we know that these
two lines are parallel.

00:00:22.990 --> 00:00:24.365
We know if two
lines are parallel

00:00:24.365 --> 00:00:26.770
and we have a transversal
that corresponding angles are

00:00:26.770 --> 00:00:28.290
going to be congruent.

00:00:28.290 --> 00:00:29.980
So that angle is
going to correspond

00:00:29.980 --> 00:00:31.790
to that angle right over there.

00:00:31.790 --> 00:00:32.880
And we're done.

00:00:32.880 --> 00:00:36.180
We have one angle
in triangle AEC that

00:00:36.180 --> 00:00:38.940
is congruent to
another angle in BDC,

00:00:38.940 --> 00:00:40.760
and then we have
this angle that's

00:00:40.760 --> 00:00:44.360
obviously congruent to itself
that's in both triangles.

00:00:44.360 --> 00:00:48.270
So both triangles have a
pair of corresponding angles

00:00:48.270 --> 00:00:50.320
that are congruent, so
they must be similar.

00:00:50.320 --> 00:00:57.050
So we can write,
triangle ACE is going

00:00:57.050 --> 00:00:58.590
to be similar to
triangle-- and we

00:00:58.590 --> 00:01:00.490
want to get the letters
in the right order.

00:01:00.490 --> 00:01:03.030
So where the blue angle is
here, the blue angle there

00:01:03.030 --> 00:01:06.100
is vertex B. Then we go
to the wide angle, C,

00:01:06.100 --> 00:01:11.250
and then we go to the unlabeled
angle right over there, BCD.

00:01:11.250 --> 00:01:12.667
So we did that first one.

00:01:12.667 --> 00:01:14.250
Now let's do this
one right over here.

00:01:14.250 --> 00:01:16.210
This is kind of
similar, but it looks,

00:01:16.210 --> 00:01:19.030
just superficially looking at
it, that YZ is definitely not

00:01:19.030 --> 00:01:21.380
parallel to ST. So we
won't be able to do

00:01:21.380 --> 00:01:23.970
this corresponding
angle argument,

00:01:23.970 --> 00:01:26.360
especially because they didn't
even label it as parallel.

00:01:26.360 --> 00:01:28.871
And so you don't want to look
at things just by the way

00:01:28.871 --> 00:01:29.370
they look.

00:01:29.370 --> 00:01:30.770
You definitely want to
say, what am I given,

00:01:30.770 --> 00:01:31.760
and what am I not given?

00:01:31.760 --> 00:01:33.080
If these weren't
labeled parallel,

00:01:33.080 --> 00:01:34.830
we wouldn't be able
to make the statement,

00:01:34.830 --> 00:01:36.390
even if they looked parallel.

00:01:36.390 --> 00:01:38.920
One thing we do have is that
we have this angle right here

00:01:38.920 --> 00:01:40.820
that's common to
the inner triangle

00:01:40.820 --> 00:01:43.000
and to the outer
triangle, and they've

00:01:43.000 --> 00:01:44.770
given us a bunch of sides.

00:01:44.770 --> 00:01:47.520
So maybe we can use
SAS for similarity,

00:01:47.520 --> 00:01:50.250
meaning if we can show
the ratio of the sides

00:01:50.250 --> 00:01:52.260
on either side of
this angle, if they

00:01:52.260 --> 00:01:55.210
have the same ratio from the
smaller triangle to the larger

00:01:55.210 --> 00:01:58.950
triangle, then we
can show similarity.

00:01:58.950 --> 00:02:02.670
So let's go, and we have to go
on either side of this angle

00:02:02.670 --> 00:02:03.360
right over here.

00:02:03.360 --> 00:02:06.960
Let's look at the shorter side
on either side of this angle.

00:02:06.960 --> 00:02:09.373
So the shorter side
is two, and let's look

00:02:09.373 --> 00:02:10.789
at the shorter
side on either side

00:02:10.789 --> 00:02:12.880
of the angle for
the larger triangle.

00:02:12.880 --> 00:02:16.190
Well, then the shorter side
is on the right-hand side,

00:02:16.190 --> 00:02:18.496
and that's going to be XT.

00:02:18.496 --> 00:02:20.120
So what we want to
compare is the ratio

00:02:20.120 --> 00:02:21.810
between-- let me
write it this way.

00:02:21.810 --> 00:02:29.500
We want to see, is XY
over XT equal to the ratio

00:02:29.500 --> 00:02:31.370
of the longer side?

00:02:31.370 --> 00:02:33.770
Or if we're looking relative
to this angle, the longer

00:02:33.770 --> 00:02:36.540
of the two, not necessarily
the longest of the triangle,

00:02:36.540 --> 00:02:38.040
although it looks
like that as well.

00:02:38.040 --> 00:02:43.792
Is that equal to the ratio of
XZ over the longer of the two

00:02:43.792 --> 00:02:45.750
sides-- when you're
looking at this angle right

00:02:45.750 --> 00:02:47.208
here, on either
side of that angle,

00:02:47.208 --> 00:02:49.746
for the larger
triangle-- over XS?

00:02:51.764 --> 00:02:54.180
And it's a little confusing,
because we've kind of flipped

00:02:54.180 --> 00:02:56.400
which side, but I'm just
thinking about the shorter

00:02:56.400 --> 00:02:59.340
side on either side of
this angle in between,

00:02:59.340 --> 00:03:01.899
and then the longer side on
either side of this angle.

00:03:01.899 --> 00:03:04.190
So these are the shorter
sides for the smaller triangle

00:03:04.190 --> 00:03:05.430
and the larger triangle.

00:03:05.430 --> 00:03:08.740
These are the longer sides
for the smaller triangle

00:03:08.740 --> 00:03:10.240
and the larger triangle.

00:03:10.240 --> 00:03:11.610
And we see XY.

00:03:11.610 --> 00:03:12.870
This is two.

00:03:12.870 --> 00:03:17.400
XT is 3 plus 1 is 4.

00:03:17.400 --> 00:03:24.160
XZ is 3, and XS is 6.

00:03:24.160 --> 00:03:25.810
So you have 2 over
4, which is 1/2,

00:03:25.810 --> 00:03:28.080
which is the same thing as 3/6.

00:03:28.080 --> 00:03:31.090
So the ratio between
the shorter sides

00:03:31.090 --> 00:03:33.160
on either side of the
angle and the longer

00:03:33.160 --> 00:03:36.300
sides on either side of the
angle, for both triangles,

00:03:36.300 --> 00:03:40.590
the ratio is the same.

00:03:40.590 --> 00:03:44.437
So by SAS we know that the
two triangles are congruent.

00:03:44.437 --> 00:03:46.770
But we have to be careful on
how we state the triangles.

00:03:46.770 --> 00:03:51.264
We want to make sure we get
the corresponding sides.

00:03:51.264 --> 00:03:52.680
And I'm running
out of space here.

00:03:52.680 --> 00:03:54.480
Let me write it
right above here.

00:03:54.480 --> 00:04:04.250
We can write that triangle
XYZ is similar to triangle--

00:04:04.250 --> 00:04:07.380
so we started up at X, which
is the vertex at the angle,

00:04:07.380 --> 00:04:09.560
and we went to the
shorter side first.

00:04:09.560 --> 00:04:11.370
So now we want to
start at X and go

00:04:11.370 --> 00:04:14.430
to the shorter side
on the large triangle.

00:04:14.430 --> 00:04:15.404
So you go to XTS.

00:04:19.899 --> 00:04:23.454
XYZ is similar to XTS.

00:04:23.454 --> 00:04:25.120
Now, let's look at
this right over here.

00:04:25.120 --> 00:04:28.860
So in our larger triangle,
we have a right angle here,

00:04:28.860 --> 00:04:31.980
but we really know
nothing about what's

00:04:31.980 --> 00:04:33.930
going on with any of
these smaller triangles

00:04:33.930 --> 00:04:35.390
in terms of their actual angles.

00:04:35.390 --> 00:04:37.140
Even though this looks
like a right angle,

00:04:37.140 --> 00:04:38.540
we cannot assume it.

00:04:38.540 --> 00:04:42.090
And if we look at this smaller
triangle right over here,

00:04:42.090 --> 00:04:44.130
it shares one side with
the larger triangle,

00:04:44.130 --> 00:04:45.770
but that's not enough
to do anything.

00:04:45.770 --> 00:04:47.710
And then this triangle over
here also shares another side,

00:04:47.710 --> 00:04:49.221
but that also
doesn't do anything.

00:04:49.221 --> 00:04:50.970
So we really can't
make any statement here

00:04:50.970 --> 00:04:52.590
about any kind of similarity.

00:04:52.590 --> 00:04:54.280
So there's no similarity
going on here.

00:04:57.500 --> 00:04:59.300
There are some shared angles.

00:04:59.300 --> 00:05:01.723
This guy-- they both share
that angle, the larger triangle

00:05:01.723 --> 00:05:02.690
and the smaller triangle.

00:05:02.690 --> 00:05:04.110
So there could be a
statement of similarity

00:05:04.110 --> 00:05:06.260
we could make if we knew
that this definitely

00:05:06.260 --> 00:05:07.360
was a right angle.

00:05:07.360 --> 00:05:09.276
Then we could make some
interesting statements

00:05:09.276 --> 00:05:10.740
about similarity,
but right now, we

00:05:10.740 --> 00:05:14.130
can't really do anything as is.

00:05:14.130 --> 00:05:16.214
Let's try this one out,
this pair right over here.

00:05:16.214 --> 00:05:18.255
So these are the first
ones that we have actually

00:05:18.255 --> 00:05:19.610
separated out the triangles.

00:05:19.610 --> 00:05:21.910
So they've given us the three
sides of both triangles.

00:05:21.910 --> 00:05:23.590
So let's just figure
out if the ratios

00:05:23.590 --> 00:05:26.460
between corresponding
sides are a constant.

00:05:26.460 --> 00:05:28.580
So let's start with
the short side.

00:05:28.580 --> 00:05:30.370
So the short side here is 3.

00:05:30.370 --> 00:05:33.960
The shortest side here
is 9 square roots of 3.

00:05:33.960 --> 00:05:37.340
So we want to see whether the
ratio of 3 to 9 square roots

00:05:37.340 --> 00:05:42.220
of 3 is equal to the next
longest side over here,

00:05:42.220 --> 00:05:49.170
is 3 square roots of 3 over the
next longest side over here,

00:05:49.170 --> 00:05:49.845
which is 27.

00:05:53.030 --> 00:05:54.820
And then see if
that's going to be

00:05:54.820 --> 00:05:59.240
equal to the ratio
of the longest side.

00:05:59.240 --> 00:06:02.590
So the longest side
here is 6, and then

00:06:02.590 --> 00:06:05.390
the longest side over here
is 18 square roots of 3.

00:06:08.070 --> 00:06:12.220
So this is going to give
us-- let's see, this is 3.

00:06:12.220 --> 00:06:15.050
Let me do this in
a neutral color.

00:06:15.050 --> 00:06:19.140
So this becomes 1 over
3 square roots of 3.

00:06:19.140 --> 00:06:26.541
This becomes 1
over root 3 over 9,

00:06:26.541 --> 00:06:28.040
which seems like a
different number,

00:06:28.040 --> 00:06:30.180
but we want to be careful here.

00:06:30.180 --> 00:06:34.690
And then this right over here--
if you divide the numerator

00:06:34.690 --> 00:06:36.170
and denominator
by 6, this becomes

00:06:36.170 --> 00:06:38.580
a 1 and this becomes
3 square roots of 3.

00:06:38.580 --> 00:06:46.940
So 1 over 3 root 3 needs to
be equal to square root of 3

00:06:46.940 --> 00:06:53.020
over 9, which needs to be equal
to 1 over 3 square roots of 3.

00:06:53.020 --> 00:06:55.220
At first they don't look
equal, but we can actually

00:06:55.220 --> 00:06:57.290
rationalize this
denominator right over here.

00:06:57.290 --> 00:07:00.130
We can show that 1 over
3 square roots of 3,

00:07:00.130 --> 00:07:02.150
if you multiply it
by square root of 3

00:07:02.150 --> 00:07:04.250
over square root
of 3, this actually

00:07:04.250 --> 00:07:06.750
gives you in the
numerator square root of 3

00:07:06.750 --> 00:07:10.140
over square root of 3 times
square root of 3 is 3, times 3

00:07:10.140 --> 00:07:11.280
is 9.

00:07:11.280 --> 00:07:13.190
So these actually
are all the same.

00:07:13.190 --> 00:07:15.082
This is actually
saying, this is 1 over 3

00:07:15.082 --> 00:07:17.540
root 3, which is the same thing
as square root of 3 over 9,

00:07:17.540 --> 00:07:19.039
which is this right
over here, which

00:07:19.039 --> 00:07:21.230
is the same thing
as 1 over 3 root 3.

00:07:21.230 --> 00:07:24.120
So actually, these
are similar triangles.

00:07:24.120 --> 00:07:25.760
So we can actually
say it, and I'll

00:07:25.760 --> 00:07:27.360
make sure I get the order right.

00:07:27.360 --> 00:07:29.600
So let's start with E,
which is between the blue

00:07:29.600 --> 00:07:31.010
and the magenta side.

00:07:31.010 --> 00:07:33.780
So that's between the
blue and the magenta side.

00:07:33.780 --> 00:07:36.010
That is H, right over here.

00:07:38.690 --> 00:07:40.500
I'll do it like this.

00:07:40.500 --> 00:07:50.830
Triangle E, and then I'll
go along the blue side, F.

00:07:50.830 --> 00:07:52.720
Actually, let me just
write it this way.

00:07:52.720 --> 00:07:57.340
Triangle EFG, we know
is similar to triangle--

00:07:57.340 --> 00:07:59.780
So E is between the blue
and the magenta side.

00:07:59.780 --> 00:08:03.180
Blue and magenta side--
that is H. And then we

00:08:03.180 --> 00:08:08.470
go along the blue side to F,
go along the blue side to I,

00:08:08.470 --> 00:08:10.660
and then you went along
the orange side to G,

00:08:10.660 --> 00:08:13.110
and then you go along
the orange side to J.

00:08:13.110 --> 00:08:18.070
So triangle EFJ-- EFG is
similar to triangle HIJ

00:08:18.070 --> 00:08:20.570
by side-side-side similarity.

00:08:20.570 --> 00:08:22.030
They're not congruent sides.

00:08:22.030 --> 00:08:24.700
They all have just the same
ratio or the same scaling

00:08:24.700 --> 00:08:25.910
factor.

00:08:25.910 --> 00:08:27.755
Now let's do this last
one, right over here.

00:08:30.120 --> 00:08:30.620
Let's see.

00:08:30.620 --> 00:08:33.309
We have an angle that's
congruent to another angle

00:08:33.309 --> 00:08:36.490
right over there, and
we have two sides.

00:08:36.490 --> 00:08:38.870
And so it might be tempting
to use side-angle-side,

00:08:38.870 --> 00:08:41.210
because we have
side-angle-side here.

00:08:41.210 --> 00:08:44.204
And even the ratios look kind
of tempting, because 4 times 2

00:08:44.204 --> 00:08:44.703
is 8.

00:08:44.703 --> 00:08:46.460
5 times 2 is 10.

00:08:46.460 --> 00:08:48.720
But it's tricky
here, because they

00:08:48.720 --> 00:08:50.315
aren't the same
corresponding sides.

00:08:50.315 --> 00:08:52.440
In order to use side-angle-side,
the two sides that

00:08:52.440 --> 00:08:54.740
have the same
corresponding ratios,

00:08:54.740 --> 00:08:56.820
they have to be on
either side of the angle.

00:08:56.820 --> 00:08:59.090
So in this case, they are
on either side of the angle.

00:08:59.090 --> 00:09:01.250
In this case, the 4 is
on one side of the angle,

00:09:01.250 --> 00:09:04.190
but the 5 is not.

00:09:04.190 --> 00:09:07.430
So because if this
5 was over here,

00:09:07.430 --> 00:09:09.605
then we could make an
argument for similarity,

00:09:09.605 --> 00:09:12.230
but with this 5 not being on the
other side of the angle-- it's

00:09:12.230 --> 00:09:14.140
not sandwiching the
angle with the 4--

00:09:14.140 --> 00:09:15.680
we can't use side-angle-side.

00:09:15.680 --> 00:09:18.800
And frankly, there's nothing
that we can do over here.

00:09:18.800 --> 00:09:20.790
So we can't make
some strong statement

00:09:20.790 --> 00:09:23.760
about similarity
for this last one.


Health care costs in US vs Europe

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:01.749
SALMAN KHAN: I'm here
with Doctor Laurence

00:00:01.749 --> 00:00:03.540
Baker from Stanford
Medical School,

00:00:03.540 --> 00:00:06.950
and we're going to talk about
health care costs, or health

00:00:06.950 --> 00:00:09.670
care economics, which
you're an expert in.

00:00:09.670 --> 00:00:12.253
LAURENCE BAKER: I like to spend
a lot of time thinking about--

00:00:12.253 --> 00:00:13.850
[INTERPOSING VOICES]

00:00:13.850 --> 00:00:15.520
SALMAN KHAN: So all
of these charts,

00:00:15.520 --> 00:00:17.700
which all seem to have
a similar shape here,

00:00:17.700 --> 00:00:19.550
these are, essentially,
measures of how much

00:00:19.550 --> 00:00:20.971
we're spending on health care.

00:00:20.971 --> 00:00:22.720
So this first one right
here, what's this?

00:00:22.720 --> 00:00:26.065
Total health spending 1960-2009.

00:00:26.065 --> 00:00:27.520
And it says, United States.

00:00:27.520 --> 00:00:28.570
LAURENCE BAKER: This
is the United States.

00:00:28.570 --> 00:00:30.819
This is data that's compiled
by the federal government

00:00:30.819 --> 00:00:33.180
every year since, well,
1960 and this figure is--

00:00:33.180 --> 00:00:35.359
SALMAN KHAN: And this isn't
adjusted for inflation.

00:00:35.359 --> 00:00:37.400
LAURENCE BAKER: That's
not adjusted for anything.

00:00:37.400 --> 00:00:39.722
That's the total dollar
value that the folks

00:00:39.722 --> 00:00:42.180
in the federal government who
like to calculate this number

00:00:42.180 --> 00:00:43.670
have come up with
for the amount we

00:00:43.670 --> 00:00:45.444
spend on health care in a year.

00:00:45.444 --> 00:00:46.110
SALMAN KHAN: OK.

00:00:46.110 --> 00:00:48.570
So someone looking just at
this data point might say, OK.

00:00:48.570 --> 00:00:50.360
Maybe it's not
inflation-adjusted.

00:00:50.360 --> 00:00:53.540
Maybe the inflation curve is
also growing at some rate here.

00:00:53.540 --> 00:00:56.130
But the absolute numbers
do seem to be large.

00:00:56.130 --> 00:01:01.460
By 2009, I guess it's
already-- well, 2009.

00:01:01.460 --> 00:01:03.340
We're already several
years passed that.

00:01:03.340 --> 00:01:04.980
two and a half
trillion dollars just

00:01:04.980 --> 00:01:06.500
to get people clear to
what we're talking about.

00:01:06.500 --> 00:01:07.410
This is in billions.

00:01:07.410 --> 00:01:10.750
This is 2,486 billion.

00:01:10.750 --> 00:01:13.520
So that's $2.4
trillion, and then

00:01:13.520 --> 00:01:18.390
that's predicted to
almost double by 2019.

00:01:18.390 --> 00:01:20.770
And our GDP is on the
order of $15 trillion.

00:01:20.770 --> 00:01:24.310
So it's a significant chunk
of everything that we produce.

00:01:24.310 --> 00:01:26.810
LAURENCE BAKER: That's a big
chunk of everything we produce.

00:01:26.810 --> 00:01:28.721
Yeah, going up rapidly.

00:01:28.721 --> 00:01:30.720
Hard to predict a little
bit, but all the trends

00:01:30.720 --> 00:01:32.370
are up and so we're
worried about--

00:01:32.370 --> 00:01:34.060
SALMAN KHAN: And this is
on a per capita basis.

00:01:34.060 --> 00:01:35.559
So I guess there's
two ways to think

00:01:35.559 --> 00:01:37.190
about why costs are going up.

00:01:37.190 --> 00:01:41.030
One is that maybe we just
have a lot more people

00:01:41.030 --> 00:01:44.610
or, that on a per person
basis, we are spending more.

00:01:44.610 --> 00:01:46.740
And this chart seems
to imply the latter.

00:01:46.740 --> 00:01:48.050
LAURENCE BAKER: This says,
on a per person basis,

00:01:48.050 --> 00:01:48.883
we're spending more.

00:01:48.883 --> 00:01:51.300
Still not inflation
adjusted in this chart.

00:01:51.300 --> 00:01:55.173
But going from
$100 or so in 1960

00:01:55.173 --> 00:01:58.450
to $8,000 in the last
couple of years--

00:01:58.450 --> 00:02:01.260
and you can see the trend
since, say, 2005 in there.

00:02:01.260 --> 00:02:03.890
It's up and it's up
pretty steeply just

00:02:03.890 --> 00:02:05.020
in the last little bit.

00:02:05.020 --> 00:02:06.130
And headed for maybe
$13,000 or $14,000.

00:02:06.130 --> 00:02:07.463
SALMAN KHAN: $13,000 or $14,000.

00:02:07.463 --> 00:02:11.030
That's a nice sub-compact
car one could buy.

00:02:11.030 --> 00:02:12.800
Not to say what's
more important.

00:02:12.800 --> 00:02:14.564
And so this next
chart right over here

00:02:14.564 --> 00:02:16.730
is actually that calculation
as a percentage of GDP.

00:02:16.730 --> 00:02:19.330
And, to me, this is, maybe, one
of the most relevant things,

00:02:19.330 --> 00:02:22.310
because that
adjusted for things.

00:02:22.310 --> 00:02:24.090
It doesn't directly
adjust for inflation

00:02:24.090 --> 00:02:26.870
but it says, as a percentage of
all of the goods and services

00:02:26.870 --> 00:02:31.162
as an economy that we are
doing, this is a percentage.

00:02:31.162 --> 00:02:32.870
So this is an interesting
one right here.

00:02:32.870 --> 00:02:36.680
So in 1960, roughly
5% of everything

00:02:36.680 --> 00:02:39.310
that all the goods and
services Americans produced,

00:02:39.310 --> 00:02:41.690
1 in 20 of that,
of our energies,

00:02:41.690 --> 00:02:43.610
was spent towards health care.

00:02:43.610 --> 00:02:47.890
And now it's looking like,
in the next few years,

00:02:47.890 --> 00:02:49.500
it's going to be
approaching 20%.

00:02:49.500 --> 00:02:51.230
It's already in the upper teens.

00:02:51.230 --> 00:02:55.040
LAURENCE BAKER: Yeah, its past
15%, 16%, and we're headed up.

00:02:55.040 --> 00:02:57.597
The last year or so, maybe,
it was a little slower growth,

00:02:57.597 --> 00:03:00.180
but you can see the trend over
the last decade or two decades.

00:03:00.180 --> 00:03:01.700
It's up up and up.

00:03:01.700 --> 00:03:03.080
So you're right.

00:03:03.080 --> 00:03:04.850
When health
economists, when people

00:03:04.850 --> 00:03:06.924
who think about
this more deeply,

00:03:06.924 --> 00:03:08.590
want to think about
health care spending

00:03:08.590 --> 00:03:10.000
two and a half trillion
is an interesting number.

00:03:10.000 --> 00:03:11.291
8,000 is an interesting number.

00:03:11.291 --> 00:03:13.000
But this one captures
population growth

00:03:13.000 --> 00:03:14.880
to a large extent,
captures inflation.

00:03:14.880 --> 00:03:18.210
And the fact that we're
spending one seventh, roughly,

00:03:18.210 --> 00:03:20.920
of our productive capacity on
health care is interesting--

00:03:20.920 --> 00:03:22.700
SALMAN KHAN: And closely
approaching-- actually, it's

00:03:22.700 --> 00:03:24.241
already one sixth
and approaching one

00:03:24.241 --> 00:03:28.860
fifth of everything that
we do is about health care.

00:03:28.860 --> 00:03:31.570
And I guess there's a
couple of things there.

00:03:31.570 --> 00:03:34.720
Maybe we're getting healthier,
I guess, is one possibility.

00:03:34.720 --> 00:03:37.399
Or maybe we aren't and
then something is weird.

00:03:37.399 --> 00:03:39.940
LAURENCE BAKER: Well, that's
the really interesting question.

00:03:39.940 --> 00:03:41.440
We can think about
why this is going up,

00:03:41.440 --> 00:03:42.815
but at the end of
the day, you're

00:03:42.815 --> 00:03:44.320
happy if we're
spending this much

00:03:44.320 --> 00:03:46.440
and if we're spending
more than other countries,

00:03:46.440 --> 00:03:48.020
we're spending more
than we did last year,

00:03:48.020 --> 00:03:49.710
if we're getting
healthier because of it

00:03:49.710 --> 00:03:51.035
or if we're getting happier.

00:03:51.035 --> 00:03:53.160
Interesting question if we
want to count happiness.

00:03:53.160 --> 00:03:55.576
It doesn't make us healthy,
but if we're getting something

00:03:55.576 --> 00:03:57.952
we value, and we're getting
worried, and we get worried--

00:03:57.952 --> 00:03:59.867
SALMAN KHAN: There are
many forms of happiness

00:03:59.867 --> 00:04:01.090
that do not make you healthy.

00:04:01.090 --> 00:04:02.327
[LAUGHTER]

00:04:02.327 --> 00:04:03.910
LAURENCE BAKER: At
the end of the day,

00:04:03.910 --> 00:04:06.190
this may be our
biggest question.

00:04:06.190 --> 00:04:09.710
SALMAN KHAN: Some will act
directly against your health.

00:04:09.710 --> 00:04:12.426
And that goes straight
into this chart

00:04:12.426 --> 00:04:13.550
which you're talking about.

00:04:13.550 --> 00:04:16.240
Maybe we should or maybe we
shouldn't compare ourselves

00:04:16.240 --> 00:04:17.275
to other countries.

00:04:17.275 --> 00:04:19.399
And this is comparing
ourselves to other countries.

00:04:19.399 --> 00:04:20.648
So this chart right over here.

00:04:20.648 --> 00:04:22.050
This is the blue graph.

00:04:22.050 --> 00:04:24.807
So we are this light
blue [INAUDIBLE] same.

00:04:24.807 --> 00:04:25.390
So this is us.

00:04:25.390 --> 00:04:28.150
This is the United
States right over here.

00:04:28.150 --> 00:04:29.580
That is us, the United States.

00:04:29.580 --> 00:04:32.740
And if we compare to other
developed countries with,

00:04:32.740 --> 00:04:35.270
I guess, not too
different demographics--

00:04:35.270 --> 00:04:37.520
LAURENCE BAKER: Yeah, the
overall developed countries,

00:04:37.520 --> 00:04:38.978
industrialized
countries, countries

00:04:38.978 --> 00:04:42.110
where the standard of living
is in pretty good shape.

00:04:42.110 --> 00:04:44.990
SALMAN KHAN: They have a
broad-- it's not a homogeneous--

00:04:44.990 --> 00:04:46.698
LAURENCE BAKER: Not
entirely homogeneous.

00:04:46.698 --> 00:04:49.240
Some people will argue the
US is more diverse than--

00:04:49.240 --> 00:04:51.090
SALMAN KHAN: The United
Kingdom is quite--

00:04:51.090 --> 00:04:52.850
LAURENCE BAKER: --pretty
diverse countries, generally.

00:04:52.850 --> 00:04:54.350
Certainly countries
with immigration

00:04:54.350 --> 00:04:56.492
issues that the US has,
countries with lower income

00:04:56.492 --> 00:04:58.450
and higher income
populations that the US does.

00:04:58.450 --> 00:04:59.533
So they're pretty diverse.

00:04:59.533 --> 00:05:01.750
SALMAN KHAN: Right, I mean,
when you look at this,

00:05:01.750 --> 00:05:04.150
maybe this is the
real chart to look at,

00:05:04.150 --> 00:05:06.000
because this is the
percentage of GDP

00:05:06.000 --> 00:05:08.330
but also puts it in
context of other countries.

00:05:08.330 --> 00:05:12.170
And that's where they're all
kind of bundled around in this,

00:05:12.170 --> 00:05:13.540
I don't know, the low end.

00:05:13.540 --> 00:05:15.665
What is this, actually,
the UK-- I didn't realize--

00:05:15.665 --> 00:05:18.270
is actually at the low end
as a percentage of GDP.

00:05:18.270 --> 00:05:21.505
And France is at
the high end of GDP.

00:05:21.505 --> 00:05:23.630
LAURENCE BAKER: Yeah, so
I've done a little picking

00:05:23.630 --> 00:05:25.080
and choosing of the
European countries.

00:05:25.080 --> 00:05:26.996
Yeah, there are some
that are a little higher,

00:05:26.996 --> 00:05:28.692
but nobody comes
close to the US.

00:05:28.692 --> 00:05:29.650
These are the big ones.

00:05:29.650 --> 00:05:31.850
UK is the lowest in
the world, really,

00:05:31.850 --> 00:05:34.600
of the developed countries,
the European countries.

00:05:34.600 --> 00:05:37.230
And France, Germany,
Canada, are commonly

00:05:37.230 --> 00:05:39.250
compared to the
US at 10% or 11%.

00:05:39.250 --> 00:05:43.060
So we're 50% higher,
60% higher than those

00:05:43.060 --> 00:05:45.249
double what's
going on in the UK.

00:05:45.249 --> 00:05:47.290
SALMAN KHAN: And do we
know why we're doing this?

00:05:49.747 --> 00:05:50.580
Where is that going?

00:05:50.580 --> 00:05:53.130
Where are we spending money that
these other countries aren't?

00:05:53.130 --> 00:05:54.550
LAURENCE BAKER:
Right, so two places.

00:05:54.550 --> 00:05:56.091
Ultimately, the
economics of it would

00:05:56.091 --> 00:05:58.795
say, if you're spending
more than somebody else, how

00:05:58.795 --> 00:06:01.170
much stuff you buying, what
kind of things you're buying,

00:06:01.170 --> 00:06:03.390
and then the price that
you're paying per thing.

00:06:03.390 --> 00:06:07.170
So we're talking either
about prices or quantities.

00:06:07.170 --> 00:06:08.540
So it's a little bit of both.

00:06:08.540 --> 00:06:12.350
If you compare us
across countries,

00:06:12.350 --> 00:06:14.700
we buy more of some
kinds of services

00:06:14.700 --> 00:06:16.210
than other countries buy.

00:06:16.210 --> 00:06:18.427
There's some interesting
comparisons--

00:06:18.427 --> 00:06:20.510
SALMAN KHAN: So we might
get more MRI's per person

00:06:20.510 --> 00:06:21.500
or something like that.

00:06:21.500 --> 00:06:23.780
LAURENCE BAKER: We certainly
do get more MRI's per person.

00:06:23.780 --> 00:06:24.490
It's interesting.

00:06:24.490 --> 00:06:26.960
It's not that we have more
doctors per capita, say,

00:06:26.960 --> 00:06:28.660
or more hospital
beds per capita.

00:06:28.660 --> 00:06:31.140
It's not that we get more
primary care visits in the US.

00:06:31.140 --> 00:06:33.490
It's actually true that,
in many European countries,

00:06:33.490 --> 00:06:35.262
you get more primary
care visits, more

00:06:35.262 --> 00:06:37.636
time with your primary care
doctor then we get in the US.

00:06:37.636 --> 00:06:40.920
But if you were
picking a poster child,

00:06:40.920 --> 00:06:43.450
it might be the MRI or
something more sophisticated,

00:06:43.450 --> 00:06:46.130
something more expensive,
specialists visits,

00:06:46.130 --> 00:06:48.670
lots of tests, and
things like that,

00:06:48.670 --> 00:06:51.450
that we buy in the United States
that they don't buy in Europe.

00:06:51.450 --> 00:06:54.320
And that drives up
our health care costs.

00:06:54.320 --> 00:06:56.290
SALMAN KHAN: So we
definitely are buying more

00:06:56.290 --> 00:06:58.059
and it's costing us more for--

00:06:58.059 --> 00:06:59.600
LAURENCE BAKER: And
the price is also

00:06:59.600 --> 00:07:00.967
different in the United States.

00:07:00.967 --> 00:07:03.050
There's some people who
have done studies of this.

00:07:03.050 --> 00:07:04.390
There's always
little bits of debate

00:07:04.390 --> 00:07:06.240
about how you define
these prices exactly,

00:07:06.240 --> 00:07:09.977
but we pay doctors--
if you're finding

00:07:09.977 --> 00:07:11.560
doctors' annual
incomes, they're going

00:07:11.560 --> 00:07:12.660
to be higher in
the United States.

00:07:12.660 --> 00:07:14.868
That is to say, we're paying,
in some sense, a higher

00:07:14.868 --> 00:07:17.540
price for a year of work from a
doctor than they pay in Europe.

00:07:17.540 --> 00:07:21.920
We're paying a higher price for
our hospital administration,

00:07:21.920 --> 00:07:25.140
for our staff in the hospitals,
things we tend to pay more.

00:07:25.140 --> 00:07:26.970
So we buy more things.

00:07:26.970 --> 00:07:29.040
We tend to buy more of
the more expensive things.

00:07:29.040 --> 00:07:30.614
And we tend to pay
a higher price.

00:07:30.614 --> 00:07:32.030
SALMAN KHAN: Do
you know, roughly,

00:07:32.030 --> 00:07:34.100
how much of the
health care dollar

00:07:34.100 --> 00:07:38.060
goes towards salaries
versus drugs versus things

00:07:38.060 --> 00:07:42.470
like MRI's and the kind of fixed
costs like MRI's and hospital

00:07:42.470 --> 00:07:43.620
beds and things like that?

00:07:43.620 --> 00:07:45.995
LAURENCE BAKER: Yeah, so some
of this you can figure out.

00:07:45.995 --> 00:07:49.770
We could almost put another
slide up on there on the screen

00:07:49.770 --> 00:07:51.265
there.

00:07:51.265 --> 00:07:53.620
The US health accounts
will tell you something

00:07:53.620 --> 00:07:57.880
like doctors and hospitals
and drugs-- drugs, 10% or 15%,

00:07:57.880 --> 00:07:59.190
a little less than that.

00:07:59.190 --> 00:08:02.070
I would have to go back and
look at the data on physicians.

00:08:02.070 --> 00:08:09.160
But physicians-- let's say that
hospitals and physicians are

00:08:09.160 --> 00:08:14.810
20% or 30%-- I hesitate to
give you look the number.

00:08:14.810 --> 00:08:15.960
SALMAN KHAN: It's not 90%

00:08:15.960 --> 00:08:16.930
LAURENCE BAKER: It's not 90%.

00:08:16.930 --> 00:08:18.070
SALMAN KHAN: When
we say hospitals--

00:08:18.070 --> 00:08:20.180
so that includes
outpatient and inpatient?

00:08:20.180 --> 00:08:22.260
LAURENCE BAKER:
Yeah, so there's lots

00:08:22.260 --> 00:08:25.140
of ways these health
accounts get broken up,

00:08:25.140 --> 00:08:29.730
physicians, hospitals, emergency
departments, different kinds

00:08:29.730 --> 00:08:32.360
of equipment and things that
get purchased, there's research

00:08:32.360 --> 00:08:33.919
and there's buildings,
and all that--

00:08:33.919 --> 00:08:36.150
SALMAN KHAN: So just
[INAUDIBLE] none of these things

00:08:36.150 --> 00:08:37.314
do make up the bulk of it.

00:08:37.314 --> 00:08:38.730
We had a video
about drug pricing,

00:08:38.730 --> 00:08:40.659
but drug pricing by
itself is not the reason

00:08:40.659 --> 00:08:42.840
why we're out here.

00:08:42.840 --> 00:08:45.780
And physician pay by
itself is not the reason

00:08:45.780 --> 00:08:48.070
why we're out there.

00:08:48.070 --> 00:08:49.910
All of these are contributing.

00:08:49.910 --> 00:08:53.066
All of these we're getting
more of and we're paying for.

00:08:53.066 --> 00:08:54.190
LAURENCE BAKER: It's a mix.

00:08:54.190 --> 00:08:54.970
At the end of the
day, it's going

00:08:54.970 --> 00:08:57.290
to be a bunch of things like
this all thrown together.

00:08:57.290 --> 00:08:58.540
We buy more stuff.

00:08:58.540 --> 00:09:00.180
We tend to buy more
expensive stuff.

00:09:00.180 --> 00:09:02.150
We buy it from people
who we pay a lot.

00:09:02.150 --> 00:09:03.420
We buy more specialist visits.

00:09:03.420 --> 00:09:05.240
For example, in the
US, we pay specialists

00:09:05.240 --> 00:09:08.160
a higher annual salary
than we pay generalists,

00:09:08.160 --> 00:09:09.840
and that comes
out in the prices.

00:09:09.840 --> 00:09:11.200
SALMAN KHAN: They don't
do that in Europe?

00:09:11.200 --> 00:09:12.120
LAURENCE BAKER:
Europe does pay more,

00:09:12.120 --> 00:09:13.790
but everybody is shifted down.

00:09:13.790 --> 00:09:15.364
All the physicians
are shifted down.

00:09:15.364 --> 00:09:17.030
And I think the
specialists are probably

00:09:17.030 --> 00:09:21.010
shifted down more in Europe
than the generalists are.

00:09:21.010 --> 00:09:22.930
We pay more for our
prescription drugs here.

00:09:22.930 --> 00:09:24.050
We pay more for--

00:09:24.050 --> 00:09:25.591
SALMAN KHAN: Now,
what are we getting

00:09:25.591 --> 00:09:27.716
in terms-- other than more
Mercedes in the doctors'

00:09:27.716 --> 00:09:28.257
parking lots.

00:09:28.257 --> 00:09:28.920
I'm kidding.

00:09:28.920 --> 00:09:29.775
I'm kidding.

00:09:29.775 --> 00:09:33.260
Although, you do
see a lot of those.

00:09:33.260 --> 00:09:36.030
It seems to be the car of
choice when I visit the doctor.

00:09:38.650 --> 00:09:41.167
And my wife's a physician.

00:09:41.167 --> 00:09:43.000
Obviously we all work
with many, so, they've

00:09:43.000 --> 00:09:45.020
worked very hard
so, I'm not going

00:09:45.020 --> 00:09:49.247
to make any statement about
they're underpaid or overpaid,

00:09:49.247 --> 00:09:51.580
especially relative to some
people I knew in the finance

00:09:51.580 --> 00:09:53.360
world, I would say that
they're definitely underpaid.

00:09:53.360 --> 00:09:54.200
LAURENCE BAKER: Possibly, yes.

00:09:54.200 --> 00:09:54.908
SALMAN KHAN: Yes.

00:09:54.908 --> 00:09:58.150
They're above Mercedes
in that world.

00:09:58.150 --> 00:10:00.800
And so are we getting
anything in exchange for this?

00:10:00.800 --> 00:10:03.117
Are we getting less wait times?

00:10:03.117 --> 00:10:04.950
Are we getting better
access to our doctors?

00:10:04.950 --> 00:10:07.030
What are we getting or
what do we know about that?

00:10:07.030 --> 00:10:08.863
LAURENCE BAKER: Well,
so this is the debate.

00:10:08.863 --> 00:10:11.260
This is in, maybe, a microcosm
one of the big debates

00:10:11.260 --> 00:10:12.640
we're having in
the US right now.

00:10:12.640 --> 00:10:13.830
We're spending more every year.

00:10:13.830 --> 00:10:15.538
We're spending more
than other countries.

00:10:15.538 --> 00:10:18.197
If it was clear we were twice
as well off, twice as happy--

00:10:18.197 --> 00:10:19.780
SALMAN KHAN: And
we're growing faster.

00:10:19.780 --> 00:10:20.920
LAURENCE BAKER: And
we're growing-- yes, it

00:10:20.920 --> 00:10:22.503
depends on how you
look at the timing,

00:10:22.503 --> 00:10:24.870
but we're growing a little
faster in some years.

00:10:24.870 --> 00:10:26.340
Our health care costs go up 10%.

00:10:26.340 --> 00:10:28.580
If we knew we were 10% happier
this year with our health care

00:10:28.580 --> 00:10:29.730
system, we would be happy.

00:10:29.730 --> 00:10:31.950
And that's the big debate.

00:10:31.950 --> 00:10:34.614
There are some cases
where the US-- there

00:10:34.614 --> 00:10:35.780
are things you can point to.

00:10:35.780 --> 00:10:38.790
We have fewer waiting
lines for some services,

00:10:38.790 --> 00:10:40.260
and some of the
countries that keep

00:10:40.260 --> 00:10:42.769
the costs down have more lines.

00:10:42.769 --> 00:10:44.310
It's also not the
case that they have

00:10:44.310 --> 00:10:46.430
waiting lines for everything
and the really serious stuff

00:10:46.430 --> 00:10:48.230
doesn't tend to have
long waiting lines.

00:10:48.230 --> 00:10:52.390
We get easier access to some
of the high tech stuff, which

00:10:52.390 --> 00:10:54.390
we like it, and so that
drives up our spending

00:10:54.390 --> 00:10:56.159
but maybe makes us happy.

00:10:56.159 --> 00:10:58.450
SALMAN KHAN: It may or may
not lead to better outcomes.

00:10:58.450 --> 00:10:59.825
So it makes us
happy that we feel

00:10:59.825 --> 00:11:02.300
like we're getting
better customer service.

00:11:02.300 --> 00:11:03.505
Instead of waiting three
months for a procedure,

00:11:03.505 --> 00:11:06.046
we're getting it in three weeks,
which would make me happier.

00:11:06.046 --> 00:11:08.560
I mean, objectively, I would
be much happier about that.

00:11:08.560 --> 00:11:12.140
But what happens when we
look at the overall outcomes?

00:11:12.140 --> 00:11:15.700
Life expectancy, and people
dying from heart disease,

00:11:15.700 --> 00:11:17.267
or whatever?

00:11:17.267 --> 00:11:19.100
LAURENCE BAKER: This
is kind of a mixed bag.

00:11:19.100 --> 00:11:21.370
Some of the most
commonly cited figures

00:11:21.370 --> 00:11:23.200
are cases where
the US doesn't do

00:11:23.200 --> 00:11:25.727
as well as some
European countries.

00:11:25.727 --> 00:11:28.310
We spend a lot more and we don't
do better on life expectancy.

00:11:28.310 --> 00:11:30.260
We don't do better
an infant mortality.

00:11:30.260 --> 00:11:32.720
There are some cases where
the US does really well,

00:11:32.720 --> 00:11:36.174
especially things where
access to the high end stuff

00:11:36.174 --> 00:11:37.090
can make a difference.

00:11:37.090 --> 00:11:38.673
And so there are
some situations where

00:11:38.673 --> 00:11:41.545
it looks like we buy the kinds
of things that are really

00:11:41.545 --> 00:11:42.670
going to make us healthier.

00:11:42.670 --> 00:11:44.670
But it's not across the board.

00:11:44.670 --> 00:11:46.310
And some of the really
interesting ones

00:11:46.310 --> 00:11:48.500
are cases where there's
fairly inexpensive stuff

00:11:48.500 --> 00:11:51.300
that looks like it would work
well and improve outcomes,

00:11:51.300 --> 00:11:53.959
and sometimes we're not
doing the inexpensive stuff

00:11:53.959 --> 00:11:55.250
that other countries are doing.

00:11:55.250 --> 00:11:59.290
And it's coming out
to maybe hurt us.

00:11:59.290 --> 00:12:02.180
We wouldn't be having the debate
if we were clearly better off,

00:12:02.180 --> 00:12:04.680
but it's really the case that,
in only some of the measures,

00:12:04.680 --> 00:12:05.670
do we end up better off.

00:12:05.670 --> 00:12:07.336
We don't always
vaccinate our kids more.

00:12:07.336 --> 00:12:09.040
We don't always get
people screened more

00:12:09.040 --> 00:12:10.680
for cancers and
things like that.

00:12:10.680 --> 00:12:12.200
But sometimes we do.

00:12:12.200 --> 00:12:14.170
So there are success
stories here.

00:12:14.170 --> 00:12:15.830
SALMAN KHAN: Now,
one thing that's

00:12:15.830 --> 00:12:17.470
interesting about looking
at this chart a little bit

00:12:17.470 --> 00:12:19.720
deeper is that it doesn't
look like this is something

00:12:19.720 --> 00:12:21.594
that, you know, since
the American Revolution

00:12:21.594 --> 00:12:24.117
that we've been spending
double as a percentage of GDP

00:12:24.117 --> 00:12:25.200
relative to everyone else.

00:12:25.200 --> 00:12:27.210
I mean if I just look at
this chart right here,

00:12:27.210 --> 00:12:30.110
it seems like us and
Canada, we were right along

00:12:30.110 --> 00:12:33.180
very similar to each other
to about the early '70s.

00:12:33.180 --> 00:12:35.405
And then we're still
in kind of that pack

00:12:35.405 --> 00:12:37.210
with Germany and France.

00:12:37.210 --> 00:12:39.680
I guess, relative to the
UK, we actually always

00:12:39.680 --> 00:12:40.570
have been higher.

00:12:40.570 --> 00:12:43.010
But then right around
this time period,

00:12:43.010 --> 00:12:45.190
the late '70s,
early '80s-- that's

00:12:45.190 --> 00:12:47.290
where we really
started to break off.

00:12:47.290 --> 00:12:49.240
Was there some
policy shift there?

00:12:49.240 --> 00:12:51.730
LAURENCE BAKER: So there's not
a tangible, specific policy

00:12:51.730 --> 00:12:52.230
shift.

00:12:52.230 --> 00:12:55.080
What starts happening in the
US there is we start adopting

00:12:55.080 --> 00:12:57.442
and we start shifting toward
the higher-end stuff more.

00:12:57.442 --> 00:12:58.650
And some of that's the part--

00:12:58.650 --> 00:13:00.649
SALMAN KHAN: That's where
the technology started

00:13:00.649 --> 00:13:01.390
to really get--

00:13:01.390 --> 00:13:03.390
LAURENCE BAKER: I think
that's mainly the story.

00:13:03.390 --> 00:13:06.450
We started to
really-- the research

00:13:06.450 --> 00:13:09.040
in things, the development that
went on in the world, really

00:13:09.040 --> 00:13:12.500
from 1940, '50, '60, started
to produce the capacity

00:13:12.500 --> 00:13:14.430
to do new and expensive things.

00:13:14.430 --> 00:13:17.060
And the US grabbed those and
other countries in the world

00:13:17.060 --> 00:13:19.325
were less quick to
grab them, maybe,

00:13:19.325 --> 00:13:20.450
you would say more careful.

00:13:20.450 --> 00:13:22.560
Maybe you would say
too careful, too slow.

00:13:22.560 --> 00:13:26.450
But the US, as you see
there, really quickly started

00:13:26.450 --> 00:13:28.550
to put up specialized
hospitals, started

00:13:28.550 --> 00:13:30.930
to buy the fancy
equipment, and you

00:13:30.930 --> 00:13:32.960
can see what kind
of came out of it.

00:13:32.960 --> 00:13:34.070
SALMAN KHAN: And to some degree,
probably, the whole world

00:13:34.070 --> 00:13:36.490
benefited from that because
you're going back to the drug

00:13:36.490 --> 00:13:40.210
pricing or the MRI manufacturers
were able to get those returns

00:13:40.210 --> 00:13:42.710
and, hopefully,
much of that they're

00:13:42.710 --> 00:13:45.370
able to reinvest and not spend
too much on other things.

00:13:45.370 --> 00:13:47.850
But it is fueling--

00:13:47.850 --> 00:13:49.909
LAURENCE BAKER: Yeah,
the innovation-- there's

00:13:49.909 --> 00:13:52.200
always these kinds of questions
that swirl around here.

00:13:52.200 --> 00:13:53.480
If the US pays a lot
of money and that

00:13:53.480 --> 00:13:55.813
comes back into innovation
then everybody benefits from,

00:13:55.813 --> 00:13:57.854
including us, maybe it's OK.

00:13:57.854 --> 00:13:59.770
I think there are people
who debate whether we

00:13:59.770 --> 00:14:01.970
got enough innovation,
enough benefits that's

00:14:01.970 --> 00:14:05.960
tangibly related to our spending
to make our spending worth it,

00:14:05.960 --> 00:14:08.230
but there are some cases
where that probably happened.

00:14:08.230 --> 00:14:11.490
And so there's some
subtlety to the question.

00:14:11.490 --> 00:14:13.030
I always say, if
you're the Yankees

00:14:13.030 --> 00:14:16.460
and you're going to pay the
huge amount for the big payroll

00:14:16.460 --> 00:14:19.570
and the big stars, people
expect you to win every time.

00:14:19.570 --> 00:14:20.890
And that's the US's challenge.

00:14:20.890 --> 00:14:21.930
If we're going to
pay the big bucks--

00:14:21.930 --> 00:14:22.820
SALMAN KHAN: We
should show results.

00:14:22.820 --> 00:14:23.420
LAURENCE BAKER:
--we really like we

00:14:23.420 --> 00:14:25.080
want to show results every time.

00:14:25.080 --> 00:14:26.790
And sometimes we
do get the results,

00:14:26.790 --> 00:14:27.997
but it's not often enough.

00:14:27.997 --> 00:14:29.330
SALMAN KHAN: It's not ambiguous.

00:14:29.330 --> 00:14:32.020
We're not winning the
championship every year.

00:14:32.020 --> 00:14:33.830
Very interesting.