[John:] Er I've got two I've just just been two schoolkids who are not doing very well and they the end of term they've you know the teacher's said they're sort of very far behind and they need to do some work during the holidays. Now normally over each break there's not that much there's I've had a few students who say they want lessons through the holiday cut normally not that much but this
[Simon:] Mm.
[John:] this holiday everyone's saying, Ooh yeah I need some more lessons you know. I'm going away on Monday so I haven't allowed for all this [LAUGHTER] so I'm trying to []
[Simon:] Yeah.
[John:] rearrange everything to fit them it. Let's have a look at
[Simon:] This week.
[John:] then.
[Simon:] Yeah this is what wanna I I just got onto like the first lesson of it.
[John:] Okay.
[Simon:] Erm notes you see they were just er exercise that we done out of the book.
[John:] Right.
[Simon:] Erm that was week eight we started on that yeah.
[John:] You're okay on trig aren't you?
[Simon:] N n no this is one
[John:] No?
[Simon:] no this is erm where bearings and that come into it
[John:] Mm.
[Simon:] I sort of was a bit lost on me trig so that's really what I want to get to go through a bit of trig.
[John:] Right okay so are you happy with sine cos tan? You know which one's which and how to sort them out.
[Simon:] I could do with it going over.
[John:] Okay. These they'll be on the front of the paper. Erm you'll have sine you'll probably have a triangle with A B C marked on it.
[Simon:] Mm.
[John:] And it's say sine is A over B or something. The best thing to do with that are you you're more used to erm... You're more used to opposite over adjacent and things like that aren't you. Or
[Simon:] Yeah well we what I normally think you see is when we've got ninety degrees there
[John:] Yeah.
[Simon:] that's the opposite. The hypotenuse is the long one.
[John:] Right.
[Simon:] And that's the adjacent.
[John:] Okay so
[Simon:] Is that in every case?
[John:] Easy way to sort them out this with with trig or with Pythagoras you're only working with a right angles triangle. So find the right angle which is usually pretty obvious and the side opposite that the longest side is the hypotenuse which is a long word.
[Simon:] Yeah.
[John:] So it's the long side. Okay?
[Simon:] So the longest side is
[John:] So
[Simon:] the hypotenuse.
[John:] The longest side the biggest side is always opposite the biggest angle.
[Simon:] Mhm.
[John:] That's the hypotenuse. And then depends on which angle we're working with. Well if we're working with this one down here okay let's say that's forty degrees or something. The next easiest one to sort out after the hypotenuse is the one that's opposite.
[Simon:] Mhm.
[John:] So that's opposite the angle that we're working with. And the one that's left is
[Simon:] The adjacent.
[John:] must be the adjacent okay. So that'll work for every triangle.
[Simon:] Yeah....
[John:] If you'd been working with this angle instead, we didn't know that and we're trying to work with this one or we say we're interested in this angle so that will be the opposite and this would be the adjacent.
[Simon:] Mhm.
[John:] And that's where the confusion comes in that it it varies depending on which angle.
[Simon:] So just go over that again
[John:] So first of all go for your right angle.
[Simon:] Mhm.
[John:] And the hypotenuse that's the biggest
[Simon:] Yeah.
[John:] that's always going to
[Simon:] Right.
[John:] be true. The next thing to do is which angle am I working with? So this one you're working with that thirty five degrees.
[Simon:] Mhm.
[John:] This is the angle we're interested in
[Simon:] Yeah.
[John:] so if we're going to work out sine tan or cos of this angle that's its opposite
[Simon:] Yeah.
[John:] and the one left is the adjacent.
[Simon:] Right.
[John:] Same with all of these.
[Simon:] Mhm.
[John:] Now if we were looking at these the other way up right if somebody gave you the triangle
[Simon:] Yeah.
[John:] and they said I want to work out this angle.
[Simon:] Mhm.
[John:] Well there's you right angle that's still the hypotenuse which one would be the opposite now if we're dealing with with this angle?
[Simon:] Er for dealing with that a that'd be the opposite yeah
[John:] That's it that's opposite and the one left is
[Simon:] Adjacent.
[John:] Okay same
[Simon:] Yeah.
[John:] if we were working with that. So the opposite is the one opposite the angle.
[Simon:] Right.
[John:] Right.
[Simon:] Just write that down for us. So it's the one opposite the angle.
[John:] first of all... go for the right angle sort out the hypotenuse okay. And then work out which angle
[Simon:] Yeah.
[John:] you're going to deal with.
[Simon:] Right....
[John:] Which angle has the... sine cos or tan... right and then that's two if you like two A work out the angle and then two B work out which is the opposite.
[Simon:] Mhm. The opposite is always opposite the
[John:] Opposite the angle.
[Simon:] angle yeah.
[John:] Okay. Work out the opposite and then three the adjacent sorts itself out then.
[Simon:] Yeah.
[John:] The adjacent is the one left over.
[Simon:] Mhm.
[John:] That'll work for that'll work every time.
[Simon:] Right.
[John:] So you won't you know you know you won't be,
[Simon:] Mm.
[John:] Ah now which one am I supposed to be using here?
[Simon:] Yeah.
[John:] Okay.
[Simon:] Okay.
[John:] So front of your sheet you will have things like sine is A over B or things like that just write on the front of your sheet and convert it so that you've got sine is equal to what do you know what sine is?...
[Simon:] Sine erm... no I should really brush up on it. I mean I I know it's so c
[John:] mixed up. It doesn't matter cos it'll be there.
[Simon:] so c so something
[John:] Silly old cow or something like that some people remember it.
[Simon:] Yeah er.
[John:] So.
[Simon:] So ca
[John:] I'll just get this.
[Simon:] in one of these.
[John:] I think you had it near the front of your notes actually.
[Simon:] Yeah.... Let's see Pythagoras on this first one no.
[John:] No.
[Simon:] I It'll be on one of these.... See I do I get them right in the class
[John:] Good.
[Simon:] but er it tends to go a bit out of your head.
[John:] Right. Let's have a look at another one at Pythagoras as well as.
[Simon:] there was a I mean I've also been given a couple of ways to remember it but
[John:] Right you can't remember [LAUGHTER] the ways to remember it [].
[Simon:] I've got it written down somewhere but.... There you are, SOH SOH CAH TOA.
[John:] Okay
[Simon:] Japanese isn't it SOH CAH TOA.
[John:] Okay so what would what would sine be from that then?...
[Simon:] What would the sine be right so erm which one are we on.
[John:] So that's the first one sine
[Simon:] The sine is the opposite over the hypotenuse.
[John:] Good. And the cos?
[Simon:] Is the adjacent over the hypotenuse.
[John:] Yep and tan?
[Simon:] Is the opposite over the adjacent.
[John:] Okay.... But they they will be on the front of your sheet. They won't be written like that in terms of opposite
[Simon:] Not even with this new change that's happening.
[John:] Well at the moment they're putting them as just label the sides A B C and they'll say
[Simon:] Mm.
[John:] sine is A over B
[Simon:] Yeah.
[John:] cos is C over B.
[Simon:] Right.
[John:] like that. Erm it's just that it throws you a bit if you've learnt them that way. So
[Simon:] Mhm.
[John:] just label the triangle that they've got opposite over... opposite and hypotenuse and adjacent and translate what they've got written there and use those.
[Simon:] Mhm.
[John:] So if we just do one.
[Simon:] Yeah.
[John:] Erm
[Simon:] Cos I wouldn't mind doing one working out with the with the
[John:] Right.
[Simon:] Just just so I can er brush up on.
[John:] So there's a triangle and we're interested in this angle here is forty degrees say.
[Simon:] Mhm.
[John:] Okay so
[Simon:] Right all have gotta add up to a hundred and eighty hasn't it.
[John:] Right so if you'd like to label that triangle.
[Simon:] Label it right erm this' d be the opposite.
[John:] Okay.
[Simon:] This' d be the... hypotenuse and this' d be the... adjacent.
[John:] That's it right okay. So
[Simon:] That'd be ninety.
[John:] That's the ninety.
[Simon:] Yeah.
[John:] Okay.
[Simon:] Which would
[John:] So we know that erm we're standing let's say we're standing a hundred and twenty metres
[Simon:] Yeah.
[John:] away from the bottom of this building. Right now we know that the angle from where we are up to the top is forty degrees.
[Simon:] Yeah.
[John:] Right. How would you work out the height of the building?
[Simon:] I don't know.
[John:] Erm well let's let's call it H or call it opp if you like.
[Simon:] Mhm.
[John:] The height of the building is opp. Now can you see any of these
[Simon:] Oh I see. So you want to find the height
[John:] Right.
[Simon:] and you're calling it opp.
[John:] Right.
[Simon:] So... it's going to be the cosine isn't it.
[John:] Which one's got the opposite... and which which two sides which o
[Simon:] Because that hasn't got the opposite.
[John:] which ones do we which one do we know?
[Simon:] Oh I see. Yeah we know the adjacent.
[John:] Right we know the adjacent.
[Simon:] And we know the opposite.
[John:] And we're trying to find out the opp so we want something that ties up opp and adjacent. Which one is that?
[Simon:] Tangent.
[John:] Okay.
[Simon:] Right.
[John:] So we've got tan forty degrees equals opp over adjacent which is equal to well we don't know opp so we'll just leave it as opp over a hundred and twenty. Okay so if you find the tan of forty degrees.
[Simon:] Now how do I do that do I just
[John:] Oh okay you just put forty degrees in.
[Simon:] Forty f forty.
[John:] And then press tan.
[Simon:] And then the equals.
[John:] That's it.
[Simon:] Do I press that no makes no difference. That's nought point eight three nine one.
[John:] Okay leave leave that in. So it's nought point eight three nine etcetera
[Simon:] Mhm.
[John:] okay and we've got opposite over a hundred and twenty at the moment and we want we just want opposite. So what would we do to both sides of the equation what would we do to that side to turn it into opposite instead of opposite divided by a hundred and twenty....
[Simon:] Don't know
[John:] Right if think of a number any number you like
[Simon:] Yeah.
[John:] okay multiply it by ten and now divide it by ten. Back to the number you thought of
[Simon:] Ten.
[John:] Okay.
[Simon:] Yeah.
[John:] think of a number multiply it by two now divide it by two back to the number you though of.
[Simon:] Mhm.
[John:] So think of some number right divide it by a hundred and twenty now we want to get it back to the number we first thought of so what
[Simon:] Mhm.
[John:] would we multiply it by.... We thought of some number divided by one twenty now we want it go back to the number we thought of.
[Simon:] Er what would you make it one twenty?
[John:] So that's it. We just multiply it by one twenty now. any number you like divided by one twenty then multiplied by one twenty comes back to that number.
[Simon:] Mhm.
[John:] So that will just cancel out and we'll have that. Now we do it to one side of the equation so there that's one twenty write it out again nought point eight three nine etcetera is equal to opposite divided by a hundred and twenty. multiply that side by a hundred and twenty so we must do the same on the other side of the equation.
[Simon:] Mhm.
[John:] Right so we multiply this by a hundred and twenty.
[Simon:] So what if I just go.
[John:] Times it.
[Simon:] Times one two O
[John:] Okay.
[Simon:] equals one hundred point six nine.
[John:] So we've got on this side one hundred point
[Simon:] Six nine.
[John:] six nine [whispering] equals opp [].
[Simon:] So that's the height.
[John:] So the height is a hundred point six nine metres. Now you'll then have to look and see if they tell you to give it to the nearest metre or the nearest maybe the nearest maybe the nearest point one of a metre or three significant figures or three decimal places.
[Simon:] Mhm.
[John:] And make sure that you give it the way they want. Now what would that be to the nearest metre?
[Simon:] A hundred.
[John:] Would it?
[Simon:] No a hundred and one.
[John:] Right okay watch that watch the rounding if it's
[Simon:] Mm.
[John:] point five or more you round up.
[Simon:] Mhm.
[John:] So... opposite is equal to the the height. Of the building which is equal to a hundred and one metres to the nearest metre.
[Simon:] Yeah.
[John:] Now if there'd been I don't know the length of this or something.
[Simon:] Yeah.
[John:] Then you'd use it's what you do is you work out which ones do we know? Well we know
[Simon:] Mhm.
[John:] the angle and we know that so how can we it up
[Simon:] So this slightly different than looking for angles isn't it. Cos say I was looking for angles and that would've just been fifty up here wouldn't it.
[John:] Right that would be fifty.
[Simon:] Yeah.
[John:] So let's do
[Simon:] But then you wouldn't need the erm Pythagoras's theory would you for that.
[John:] If we've got if we've got the angle usually we g going to use trig.
[Simon:] Mhm.
[John:] If we've got two side but we haven't got an angle then we'll just use Pythagoras.
[Simon:] Mhm.
[John:] Okay. Have a look at this the other way up. We didn't know that angle but we
[Simon:] Mhm yeah.
[John:] knew this one was fifty. Right well this time
[Simon:] We want that'll become the
[John:] We'll get
[Simon:] opposite.
[John:] we'll get that's the that's going to be the opposite
[Simon:] That'd be the
[John:] that's still the hypotenuse that never changes. But this one would be the opposite and this one now would be the
[Simon:] ad adjacent.
[John:] Okay. that's the one looking at fifty degrees.
[Simon:] Yeah.
[John:] So this time what do we know? Well we know the opposite and we're trying to find the adjacent.
[Simon:] Mhm.
[John:] So which one of these uses opposite and adjacent?
[Simon:] Tan.
[John:] So it'll be tan again but his time we'll have tan fifty is equal to one twenty over the adjacent which is what we're trying to find....
[Simon:] Right.
[John:] Multiply both sides by adjacent. So on this side we get adjacent.
[Simon:] We've got fifty tan haven't we. Fifty tan
[John:] Okay.
[Simon:] that's one point ni one nine.
[John:] One point one nine.
[Simon:] Nine.
[John:] Okay equals a hundred and twenty over adjacent now multiply both by adjacent. Adjacent times one point one nine is equal to a hundred and twenty.
[Simon:] Yeah.
[John:] We multiply adjacent there and adjacent here. Now divide both sides by one point one nine. Adjacent times one point one nine over one point one nine equals a hundred and twenty over over one point one nine. Okay?
[Simon:] Mhm....
[John:] They cancel out so the adjacent is going to be that. So if you do if you just press ah
[Simon:] One two O
[John:] Divided by
[Simon:] divided by one point nine
[John:] Now if you just put in fifty.
[Simon:] Divided by fifty?
[John:] put fifty and then tan and now equals. Now we've divided it by the tan of fifty because you see
[Simon:] Well that comes to a hundred and sixty nine.
[John:] if you round up half way through the way you were going to do then
[Simon:] Mhm.
[John:] and just call it one point one nine
[Simon:] Mm.
[John:] you lose quite a bit of accuracy.
[Simon:] Mhm.
[John:] So again that comes to a hundred point six nine. So it doesn't matter which way you do it and which way round you do it
[Simon:] Yeah.
[John:] and which angle we work with it still come to the same thing. So you can
[Simon:] Mhm.
[John:] do it either way.
[Simon:] Yeah.
[John:] And usually you'll work with the angle that you've been given rather
[Simon:] Mm.
[John:] than working out the other one. So some of them will be given and some of them won't and you'll work out which ones can I fit in here opposite adjacent or that. Now on is that okay?
[Simon:] Yeah.
[John:] Or do you think
[Simon:] Well
[John:] could do with another one?
[Simon:] Yeah I could do with another one I think.
[John:] Okay. Er let's see if we've got.
[Simon:] You see these ones I suppose
[John:] Let's pick one out of there then.
[Simon:] Erm all he's been doing here is getting me to find the sides. See opposite hypotenuse adjacent. Opposite adjacent this is what you've been talking about the a the angle isn't it.
[John:] Okay.
[Simon:] It's only just dawned on me now how he's got to that.
[John:] Right.
[Simon:] Hypotenuse is the longest side and the opposite is opposite to the
[John:] Angle.
[Simon:] angle.
[John:] and the adjacent is the one left over.
[Simon:] Which makes that the adjacent.
[John:] That's it.
[Simon:] Yeah.
[John:] And you've got these written in here sine
[Simon:] Mm.
[John:] cos and tan.
[Simon:] We've been using the words SOH CAH TOA to help remember these. [reading] Each angle has its own unique sine cosine or tangent. This means they can be stored in a scientific calculator. [] Er
[John:] They're usually not stored they're calculated inside the calculator. The calculator
[Simon:] Yeah.
[John:] has a little program that goes chuntering away
[Simon:] Mm.
[John:] working it out.
[Simon:] Mm. Oh there are silly old Howard Kendal and his team of amateurs....
[John:] Okay can can you remember that?
[Simon:] What.
[John:] Silly old Howard Kendal and his team of amateurs.
[Simon:] Er the maths teacher in school didn't like that cos he's an Everton supporter.
[John:] Ooh. [LAUGHTER]
[Simon:] [LAUGHTER]
[John:] Right can you remember that?... As I say it will be on the front of the sheet so you can
[Simon:] I'd probably remember that easier to be honest SOH CAH TOA.
[John:] Mm SOH CAH TOA....
[Simon:] I mean... having found you know this sine is the opposite over the hypotenuse tan is basically what you've got to find I suppose is which two sides of the triangle you're using.
[John:] That's it.
[Simon:] Yeah. And so you'll look for sort of these two combinations to find out whether it'll be a tangent a cosine or a sine.
[John:] Exactly that's it
[Simon:] Yeah.
[John:] that that's all there is to it. What sides have I got here? Right and let's say in this one we had opposite and adjacent so we said where does that come there it is opposite and adjacent so it'll be tan. Now if it had been opposite and hypotenuse which one would you have used?
[Simon:] It would have been sine.
[John:] And if you'd had adjacent and hypotenuse?
[Simon:] It would've been cosine.
[John:] That's it
[Simon:] Mm.
[John:] That's that's that's all there is
[Simon:] Yeah.
[John:] to it. Once you've sort of spotted that which you have you you
[Simon:] Mm.
[John:] shouldn't have any trouble at all.
[Simon:] Yeah.
[John:] So let's just try one to sort that out. Erm here y'are we've got a lad with a kite it's fixed on the ground well let's say let's say it's fixed on the ground first of all and erm we're trying to find out how high it is and it's directly over this point which is erm... and we don't we don't know. We know it's at an angle of ooh let's use forty degrees again. The kite string is making an angle of forty degrees there and it's got a hundred metres of the line payed out. And he wants to know how high it is.
[Simon:] Mhm.
[John:] So the first thing is what what's the first thing you do?
[Simon:] Find the sides.
[John:] Okay so the first thing to go in which is pretty obvious. That's it.
[Simon:] Which would make this the opposite
[John:] Right.
[Simon:] This the adjacent and this the
[John:] Which is the one you really did first isn't it.
[Simon:] Hyp what
[John:] In fact you really did the hypotenuse first I think
[Simon:] Yeah.
[John:] cos you put the right angle in you though right
[Simon:] Yeah.
[John:] Okay so what do we know and what are we trying to find out?
[Simon:] Well we know we've got an angle of forty degrees
[John:] Okay.
[Simon:] Erm a hundred metres we want to find the height. So we want to find the opposite.
[John:] Right and what do we know which of the other sides do we know?
[Simon:] The adjacent.
[John:] Mm we don't know that do we?
[Simon:] No. Oh er the hypotenuse is at forty.
[John:] That's that's the hundred metres that's the length of his string. There's his kite on the end of that.
[Simon:] Mhm....
[John:] Okay there's a hundred metres of string out so you know
[Simon:] Yeah.
[John:] the hypotenuse. So we've got opposite and hypotenuse hypotenuse and opposite which one ties those up?
[Simon:] The hypotenuse and the opposite erm
[John:] Have a have a look cos they will be on the sheet.
[Simon:] Okay. Well it's opposite over hypotenuse is sine.
[John:] Right so just write the equation as you've got it there sine equals opposite over hypotenuse. So all
[Simon:] Yeah.
[John:] you need to write is sine of sine of forty... equals what?
[Simon:] Equals the opposite over the hypotenuse. Which is equal to... a hundred?
[John:] Well what's the opposite? We don't know that's the one we're trying to find out so we just put
[Simon:] We don't know do we yeah you wouldn't put ninety degrees would you we don't know.
[John:] No opposite that angle
[Simon:] Yeah we don't know we want the height.
[John:] That side so okay it's just
[Simon:] And
[John:] just put so just write opp. And we'll find it later.
[Simon:] Mhm.
[John:] And the hypotenuse is
[Simon:] A hundred.
[John:] Yeah.
[Simon:] Right.
[John:] So if you calculate the sine of a hundred of forty degrees now and leave it in the calculator.
[Simon:] for doing that you go forty
[John:] That's it forty and then sine....
[Simon:] helps if I put the calculator four O
[John:] Sine.
[Simon:] sine and you don't need to put press the equals do you do it's nought point six four two.
[John:] So we've got nought point six four etcetera
[Simon:] Mm.
[John:] is equal to opposite divided by a hundred. Well we don't want opposite divided by a hundred we want just opposite. So what would we multiply this thing by to turn it into just opposite?
[Simon:] [yawning] A hundred. []
[John:] That's it.... So we multiply by a hundred on that side so we must multiply by a hundred by a hundred on the other side to keep
[Simon:] Mhm.
[John:] it balanced.
[Simon:] Yeah.
[John:] What's a hundred times that come to?
[Simon:] so I'll go times one nought nought equals sixty four point two.
[John:] Sixty four point
[Simon:] two seven
[John:] Which is nearer point three.
[Simon:] Yeah.
[John:] Sixty four point two seven nine
[Simon:] Eight seven eig eight.
[John:] Oh sorry two seven eight seven six.
[Simon:] Yeah.
[John:] Two seven eight seven six etcetera is equal to That's fine so that's opposite. And it depends on what they want if they want it to three decimal places with this
[Simon:] Yeah.
[John:] they probably want it to about the nearest metre
[Simon:] Yeah.
[John:] how high is it to the nearest metre. So what would that be to the nearest metre?
[Simon:] it'd be sixty four wouldn't it.
[John:] Excellent sixty four metres is equal to the opposite
[Simon:] Right.
[John:] height.
[Simon:] Now can we
[John:] To the nearest metre. Okay.
[Simon:] Erm... It might be this might be the paper actually no I don't think it is. I don't think it's the one I was thinking of. Erm what was I thinking of. Yeah could we do number twelve?
[John:] Okay.
[Simon:] I mean I've not done it before this is
[John:] Right.
[Simon:] a paper that I.
[John:] A straight section of motorway motorway... midway between P and Q. So this is this is drawing a scale diagram.
[Simon:] Mhm.
[John:] This this isn't calculating it using sine and cos or anything.
[Simon:] Oh isn't it oh well.
[John:] But they haven't It looks as if it's a right angle there
[Simon:] Mm.
[John:] It might not be. You can't take it that it is you have to draw your scale diagram.
[Simon:] Yeah.
[John:] Now how would you draw this diagram?
[Simon:] I haven't read read the question so
[John:] Okay.
[Simon:] [reading] The diagram below shows a s straight section of motorway []
[John:] Mhm.
[Simon:] [reading] nine hundred metres long P to Q is nine hundred metres long. And a church C which is seven hundred metres from P []
[John:] Right.
[Simon:] [reading] and five hundred metres from Q. B is a bridge over the motorway midway between P and Q. []
[John:] Mhm.
[Simon:] [reading] Using a scale a one centimetre representing a hundred metres [] So that'll be nine centimetres.
[John:] Right.
[Simon:] Draw round like the point P. That'd be nine centimetres erm five centimetres and... seven centimetres.
[John:] Okay. So how would you go about doing that diagram?
[Simon:] I'd erm I wouldn't have thought of using a compass but you're right aren't you.
[John:] Okay have you do you.
[Simon:] Do you want a ruler? I've got one somewhere....
[John:] Okay so you decided on your scale and you decided it was nine centimetres along there okay and... f the way to do it fairly accurately is just draw a line that's a bit longer than nine.
[Simon:] Mhm....
[John:] And the measure off nine on it. Give yourself a starting place get the zero on that nicely
[Simon:] Mhm.
[John:] and then nine.
[Simon:] Right.
[John:] Now I've done the hard bit there straight line.
[Simon:] Yeah.
[John:] What are we going to do about this church how are you going to find out where that church C is?
[Simon:] Erm... well it's seven centimetres
[John:] Okay.
[Simon:] If I just put a point then I measured up to there
[John:] Mhm.
[Simon:] And see if I got five centimetres five.
[John:] So
[Simon:] Just say if that was seven and mm er that'd end up seven. I don't know? Er maybe I should do it on graph paper.
[John:] No cos your graph paper wouldn't show you the s at an angle.
[Simon:] No.
[John:] You could do it with two rulers couldn't you. If you put one ruler on here and kept sliding them about until it was
[Simon:] Yeah.
[John:] seven from there and five from there.
[Simon:] Mhm.
[John:] But there's a much easier way of doing it.
[Simon:] Right what what is it?
[John:] Well use your compass and just draw... that's P show me all the points that are seven hundred metres from P. Draw the draw the path of all the points that are seven hundred metres from P.
[Simon:] an idea here
[John:] Hey.
[Simon:] that there so er that's seven hundred right.
[John:] Okay.
[Simon:] And this is P.
[John:] Right.
[Simon:] Right. So if we sort of went like that
[John:] Okay.
[Simon:] that's the that's the path isn't it.
[John:] Right.
[Simon:] And if we set this on five.
[John:] Brilliant that's it okay you've got it.
[Simon:] Like that and set it on Q.
[John:] Right.
[Simon:] Right where it meets which is there.
[John:] That's it. So anywhere along there is seven... from P anywhere along this one is five from Q. And that place where they meet
[Simon:] Should be
[John:] five from Q and seven form P.
[Simon:] Should be just right then shouldn't it. Yeah so we'll go simple when you know how innit. [LAUGHTER]
[John:] It's like a lot of things if you if you do know how to do them you think what's the problem if you haven't
[Simon:] Yeah.
[John:] done them before Oh lovely thanks very much. Have you had your hair cut then?
[speaker001:] Yes [LAUGHTER] Oh you don't like it do you? [LAUGHTER]
[John:] I've I've no comment no comment. [LAUGHTER] No I I prefer longer hair for women
[Simon:] Yeah.
[John:] Yeah yeah my wife's always saying she's going to have her hair cut [LAUGHTER]
[Simon:] Yeah [LAUGHTER] yeah.
[John:] And then measure that angle it says.
[Simon:] Right now... where's where's the question oh here it is up here isn't it....
[John:] use that one or another one?
[Simon:] Now how do you measure an angle?... I'm not used to using this on a circle.... Ah hang on
[John:] Right.
[Simon:] you gotta get it somewhere like that haven't you.
[John:] Mhm.
[Simon:] Or has it gotta be on this line here?
[John:] Well the angle we're measuring is this one here what angle are we going to measure? Find the angle P C Q so.... P C Q so we're measuring this angle here. It looks very much like a right angle.
[Simon:] Mhm.
[John:] So we need this on one of the lines... yeah.
[Simon:] Yeah.
[John:] And that little cross sometimes it's a little hole on the corner on the angle itself.
[Simon:] Mhm.
[John:] Now we can measure it and it's not
[Simon:] Ninety.
[John:] not ninety it's
[Simon:] Eighty five.
[John:] What have we got have a look I mean we don't know that we've draw this completely accurately. Looks about ninety four.
[Simon:] Yeah right.
[John:] Right.
[Simon:] Yeah.
[John:] Ninety four. How could we check if it is actually ninety and we've got it wrong. That was seven wasn't it and this was er sorry that was nine that was nine
[Simon:] No that was nine, that was seven and this was five.
[John:] That's seven and that's five. How could we check if that was if that's really supposed to be ninety and we've and the drawing's not quite right. Cos that line you've drawn there.
[Simon:] It's just slightly off yeah.
[John:] Doesn't doesn't go to that point at all so that would make see how much difference that makes to the
[Simon:] Mm.
[John:] angle.
[Simon:] Yeah.
[John:] So measure that angle again. Now it's looking like about ninety one.
[Simon:] Yeah.
[John:] Ninety two ninety one ninety two
[Simon:] See and that's not quite on on that there.
[John:] And that's not quite on so that would bring it a little bit it might be about ninety two or something it might
[Simon:] Mm.
[John:] be ninety. How can we check if it is ninety?
[Simon:] Erm.
[John:] From the numbers we've got there.
[Simon:] By using one of the Pythagoras's theorem.
[John:] Okay good. So if that if that's a right angle only if it's a right angle cos Pythagoras's theorem doesn't work if it's not then we've got the easy way to remember Pythagoras is... long equals medium plus short.
[Simon:] Mhm.
[John:] I mean it's not just the long it's long squared equals medium squared plus short the the medium and the short sort of would add up to give the long.
[Simon:] Mhm.
[John:] That's one way of thinking of it. So the long one squared... Does nine squared equal seven squared plus five squared. So what's nine squared?
[Simon:] Nine nines is eighty one.
[John:] Okay yeah and seven squared?...
[Simon:] Erm... forty nine.
[John:] Alright and five squared?
[Simon:] Twenty five.
[John:] Right. What's forty nine and twenty five come to? Well it doesn't
[Simon:] Seventy four.
[John:] it doesn't come to
[Simon:] Seventy four.
[John:] Yeah seventy four it doesn't come to eighty one.
[Simon:] No.
[John:] So it's not a right angle triangle. But you look at the diagram they've given you which is not exactly the scale and they do this quite a bit. See it's about like that it's a little bit... It's it's ninety and a tiny bit
[Simon:] Yeah.
[John:] and you look at it and you think Ooh must be a right angle.
[Simon:] Mm.
[John:] And a lot of people answering that question will just assume it's a right angle
[Simon:] Yeah.
[John:] and they'll do that and sort of get very few marks on it so watch
[Simon:] Mhm.
[John:] that when you've got one that looks like a right angle and they
[Simon:] Mhm.
[John:] don't say it is.
[Simon:] Yeah.
[John:] But that way for doing Pythagoras. Erm let's have a look at a couple using Pythagoras. Let's say we've got erm... this one is... If that's thirteen... and this one is... twelve right... mm with a bit of luck that should be a right angle ish. It's not exactly a right angle it's not drawn to scale. But that's a right angle... call it X or whatever you like. Want to find that side and we know that's thirteen centimetres and that's twelve centimetres and that's a right angle how would how would you go about finding that?
[Simon:] And you want to find that side well... we get the right way wouldn't it let's see. That would sort of tell me that that was the hypotenuse and that was the adjacent.
[John:] Right okay so that's the hypotenuse.
[Simon:] Adjacent.
[John:] Ah now you haven't got an adjacent or an opposite with Pythagoras.
[Simon:] Oh no.
[John:] You've got all you've got really you've got the hypotenuse but you don't need to bother with you just can call it the long one.
[Simon:] Mhm.
[John:] And... remember your equation... long squared equals medium squared plus short squared.
[Simon:] Mhm.
[John:] Okay right which is the long one which is the longest one? Thirteen.
[Simon:] Thirteen.
[John:] So we get thirteen squared equals and what's the medium one?
[Simon:] One three times one three equals one six nine.
[John:] Okay what's the medium one.
[Simon:] And the medium one is X.
[John:] Is it? Mm.
[Simon:] On no no sorry that's the short the medium one is twelve yeah.
[John:] It doesn't matter if we get them the wrong way round it'll still work out.
[Simon:] Which is a hundred and forty four.
[John:] Plus the short one squared so
[Simon:] And the short one is X.
[John:] if we subtract twelve squared form each side. Thirteen squared minus twelve squared equals short squared. Okay.
[Simon:] Mhm.
[John:] So if you work out what thirteen squared minus twelve squared
[Simon:] So it's a hundred and sixty nine minus a hundred and forty four isn't it.
[John:] Mhm.
[Simon:] Twenty four.
[John:] Twenty?
[Simon:] Twenty five.
[John:] Right sounds okay
[Simon:] Centimetres.
[John:] That's what I that's what I got.
[Simon:] Yeah.
[John:] equals short squared.
[Simon:] So five is the short side.
[John:] Five is equal to the short side.
[Simon:] Mhm.
[John:] So that will be five centimetres.
[Simon:] Right.
[John:] Okay.
[Simon:] So if you get on an exam something like that and they're and they're saying to you A to B is sixty mile to London.
[John:] Mm.
[Simon:] What's the bearing between London and Glasgow?
[John:] Ah.
[Simon:] Like how does it
[John:] Okay so we'll fini we'll finish up with right angles first. If you're looking at triangles you're first thing you're looking at is has it got a right angle? Is there a right angle in it somewhere?... If it hasn't well you probably you've got problems.
[Simon:] Mm.
[John:] so that's your first one has it got a right angle? If it has yes we go do they give you an angle? Right let's say they do. Have they given you have they given you the length of two sides? Yeah.
[Simon:] Mhm.
[John:] Two lengths given yeah.
[Simon:] Yeah.
[John:] If so you can use Pythagoras... which is long squared equals medium squared plus short squared. To find third side. Okay?
[Simon:] Yeah.
[John:] If it isn't if you haven't got the two lengths given you've got you've got... one length plus one angle. That one angle is apart from the right angle. Right.
[Simon:] Yeah.
[John:] Apart from the.... So if you've got one length and one angle then depending on which one you've got you're going to use sine cos or tan... to find the side the length you want.
[Simon:] Mhm. that's if you've got an angle and a length.
[John:] A length and an angle you'll use the trig.
[Simon:] Yeah but otherwise.
[John:] You'll use Pythagoras. Right so if they give you two s two lengths to fine a third length the easiest way and the most accurate way is use Pythagoras.
[Simon:] Mhm.
[John:] If they give you one length and an angle then you'd use either sine or cos or tan to find the other one.
[Simon:] Right.
[John:] Sometimes on this one they might give you erm two lengths and they might ask you to find an angle.
[Simon:] Can we do one of them?
[John:] Right er they might sometimes... so that's to find a side... and this actually comes off here. Right given two sides plus right angle
[Simon:] Mhm.
[John:] Find an angle.... Again you'd use trig.
[Simon:] Yeah. Right....
[John:] opposite not opposite but opposite page.
[Simon:] Mhm....
[John:] So let's say we've got... a hill. And erm we know that we went along this hill and we went along... fifteen kilometres.... Okay?
[Simon:] Yeah.
[John:] And when we'd gone along fifteen kilometres we'd gone up by... four point eight metres.
[Simon:] Mhm.
[John:] Right what we want to find is how steep is the the hill we want to find that angle.... X degrees. How would you go about that?
[Simon:] Erm [tape ends]