00:00Hi everybody. So this is
00:02going to be a lesson
00:03on the sine rule. Now
00:04the sine rule is given
00:05to you in the formula
00:06booklet. This is it. It's
00:07A over sine A equals
00:08B over sine B equals
00:09C over sine C. Now
00:10you'll notice that you have
00:12a small A and a
00:13big A and a small
00:14B and a big B
00:15and a small C and
00:16a big C. These letters
00:18refer to this type of
00:20triangle where the little B
00:22is the length of the
00:23side and the big B
00:25is the angle. Now notice
00:27the
00:28that the B is opposite
00:30the B, and the C
00:33is opposite the C, and
00:34the A is opposite the
00:36A. Now don't let the
00:38A, B, and Cs confuse
00:40you. Just remember it's side
00:42over sign of the opposite
00:44angle equals another side over
00:45the sign of the opposite
00:46angle, it was the other
00:46side over the sign of
00:47the opposite angle. You can
00:49also flip these just using
00:51algebra. It doesn't give you
00:53this form in the formula
00:55booklet.
00:56It's definitely worth noting that
00:58sine A over A equals
01:00sine B over B equals
01:03sine C over C. This
01:06is more useful when we're
01:07going to find the angle
01:08just because it prevents you
01:13to have to rearrange it
01:14in the middle of the
01:15equation. Okay, so what is
01:18the sine, when do we
01:19use it? Well, firstly note,
01:22it's not a right, it
01:22doesn't have to be a
01:23right angle.
01:24trying to work with a
01:25right angle triangle but it
01:26doesn't have to be a
01:26right angle triangle which is
01:27great because so couture and
01:29Pythagoras' theorem limit us because
01:31it has to be a
01:32right angle triangle. The sine
01:33rule doesn't. This is when
01:35we use it. When we
01:37have two angles and one
01:39side, that's for trying to
01:41find the side. So if
01:43we want to find a
01:44side, we need two angles
01:46and one side. So here
01:48look, I have two angles,
01:50I have one side, I
01:51can find
01:52I can find this side.
01:55And if I want to
01:56find the angle, I need
01:57two sides and one angle,
01:59but not the angle between
02:02the sides. So I have
02:03these two sides and I
02:05have this angle, two sides
02:06and one angle. But if
02:07I had this angle, it
02:09actually wouldn't work because I
02:13wouldn't be able to, I'd
02:14have two unknowns in the
02:16equation, which I'll explain in
02:17a second. Okay, so first
02:18we're going to find the
02:19length.
02:20and the length, it's A
02:22over sine A equals B
02:23over sine B. Now again,
02:24I don't even use those
02:26letters A, B, and C.
02:27I just think it's side,
02:30X over sine angle. So
02:33X over sine 37 equals
02:37other side, 15 over sine
02:43102. And then I can
02:47multiply across
02:48I can go straight to
02:50numerical solve if you want,
02:52but let's multiply across just
02:53to make sure you understand
02:54how it works. 15 sine
02:5737 divided by sine 102.
03:04I can do this on
03:05my calculator. I mean degrees,
03:08yes, it's 15 times sine
03:1337.
03:16all over um sign 102.
03:20Now you could actually if
03:21you want I prefer to
03:25use this function here so
03:28it just looks nicer and
03:29then sign 102. Sign 102.
03:35Get my answer at 9
03:35.22. Not 8 .99. 2
03:39.2 .2 .8. 9. Does
03:41that look like a reasonable
03:42answer? Yeah it's reasonable
03:44It's not something crazy. So
03:46that is my answer and
03:48it's in meters. Fine, easy.
03:52Second one. So it's easy
03:55when you know it's sine
03:56rule and you know it's
03:57going to work. But often
03:58in the exam, you don't
04:00know it's, they don't say
04:01you use the sine rule.
04:02Sometimes they do, but often
04:03they won't say anything. They'll
04:05just say find the side
04:06and you need to, you
04:07need to think what rule
04:08do I have that will
04:09work here. So you're finding
04:11an angle. I need two
04:12sides.
04:12one two and an angle.
04:15I have an angle but
04:15not the one between. Fine
04:17it's not. So now I'm
04:18going to go to use
04:19this second row that I've
04:20made up. So it's sine
04:24theta. Start with the one
04:25you're looking for. Sine theta
04:27over the opposite side. What
04:30sides opposite? 10. Sine theta
04:32over 10 equals sine. Use
04:34the angle that I know.
04:3652 over 12. And then
04:40I'm going to
04:40use numerical solve for this
04:42one just to show you
04:43how nice and easy it
04:45is. I'm going to do
04:47menu algebra numerical solve and
04:51I'm going to do this
04:55function sine let's call it
04:59x sine x over 10
05:03equals sine 52
05:08Okay, actually, I should have
05:12done this. Sign 52 over
05:2012 and then I have
05:22to put comma x, so
05:24it's find x, 41 .0,
05:284, 6, 8, 41 .0,
05:324, 6, 8 and that's
05:34in degrees. Does that seem
05:36like a real
05:36reasonable answer. Yes, I think
05:39it does. Again, note how
05:41sweet is numerical solve that
05:43I can just do it
05:44in one go. But certainly,
05:46write out the equation. But
05:48that's enough. You don't need
05:50to show that next step
05:51to get all your to
05:52get all your marks. Okay,
05:53that's the sign rule. It's
05:55in the form of the
05:55booklet. It's for finding signs
05:56and angles of triangles. It
05:58doesn't have to be a
05:59right angle triangle. And these
06:00are the kind of rules
06:01for when you can use
06:03it or when it will
06:04work.
06:04And I say try as,
06:07like if you're not sure,
06:09try the sine rule and
06:10you'll quickly find out whether
06:11it will work or not.
06:13Okay, see you in the
06:13next lesson. Cosine rule.