00:02
Okay, city a is 1866 miles from city b.
00:10
So here's our a, b, c, 1866.
00:16
Obviously, this is not to scale.
00:18
City b is 771, 2435.
00:24
So little b is across, we're going to call this little b.
00:30
So angle b, we're going to do everything in green.
00:34
Angle c is across from little c, which we're going to do in blue.
00:40
Angle a is across from little a, which we're going to do in red.
00:45
So we're going to use the law of cosines in order to solve these sides.
00:54
We can use law of signs too, but we're just going to use law of cosines tonight for these.
00:58
So i'm going to find the biggest side first, so we're going to find b first.
01:02
So law of cosine says to do b squared equals a squared plus c squared minus 2ac cosine b.
01:14
But really since we're trying to find angle b, we're going to move all of these over here to get b squared minus a squared minus c squared.
01:24
And then we're going to move the minus 2a c over as well.
01:30
And also the cosine.
01:32
So we cosine to the negative 1, and that equals our b.
01:43
So really this is going to be our formula.
01:46
So this is going to be our general formula.
01:48
This is just the manipulation of our original one.
01:52
So we're going to use this for all of our formulas.
01:57
So on this, on our triangle, we're going to do to find angle b.
02:05
We're going to do cosine our little b we go back up here our little b was 2435 so that's 2435 so that's 2435 so that's 2435 minus our a was 771 oops and i forgot the squared our a was 771 and our c was 771 and our c was 1866.
02:48
And we're dividing by negative 2 times the a was 771 and the c was 1866.
03:02
And that equals b.
03:03
So in the calculator, make sure that you have your mode on degree.
03:08
And when you stick all of that in the calculator for angle b, you should get that that's 130 .1 degrees...