Pythagorean Theorem, a la Shmoop.
Peter Pan has a problem. [Peter awakens in bed]
No, no…another problem.
He’s had his shadow a long time,
and it’s been run ragged.
Time to bite the bullet…
he’s due for a new one.
But he doesn’t just want a replacement.
He’s in the market for something bigger and better. [Peter browsing a supermarket]
Michael and John have been introducing Peter
to a little pre-algebra…
…and Peter decides he can pick out his new
shadow by using the Pythagorean Theorem…
…which says that, when dealing with a right
triangle, the square of one leg of the triangle,
added to the square of the other leg, will
equal the square of the hypotenuse.
Or expressed algebraically  a-squared + b-squared = c-squared.
Fortunately for Peter, he and his shadow form
a perfect right triangle. [Peter stood with a perfect triangle and Wendy appears]
He knows that Wendy wants the tippy-top of
his head to be exactly 10 feet away from the
the top of his shadow's head at all times.
Peter is six feet tall.
His height squared is 36…
…while the desired distance from the head
of his shadow squared is 10 squared…
…or 100.
So Peter needs his shadow
to be a number that, when squared… [Floating numbers]
…makes up the difference between 100 and 36.
So let's do the math.
100 minus 36 is 64…
… and the square root of 64…is 8.
Checking to make sure that works out, we’ve got a
triangle with sides that are 6, 8 and 10 feet long… [triangle with all measurements of each side]
…and 6 squared plus 8 squared
comes out to 100…
…which is the same as 10 squared.
Peter is a lost boy no longer!
The neighbors are very jealous… [Peter in his bedroom and Captain Hook appears]
