00:01
Okay, so i'm going to solve this triangle here.
00:04
When i'm given three sides and no angles, i need to start with law of cosines.
00:08
And what i'm going to do is i'm going to use, let's do, let's just do this one first.
00:16
So if we use a squared is equal to b squared plus c squared minus two times bc times the cosine of a.
00:26
So what i can do is i can kind of solve this for a.
00:30
I'm going to do that right now.
00:31
I'm actually going to take a squared minus b.
00:33
Squared minus c squared is equal to a negative 2bc cosine of a divide both sides by a negative 2 bc so this will actually turn it into i can do b squared plus c squared minus a squared over 2bc is equal to the cosine of a which means that a is going to be the inverse cosine of all of this b squared plus c squared minus a squared over 2bc so this is what i'm going to plug in my calculator so i'm going to take the inverse cosine.
01:09
We got b squared.
01:11
So b is 12, a is 48, and then c is 51.
01:17
So i got 12 squared plus 51 squared minus 48 squared over two times 12 times 51.
01:30
Okay.
01:31
So this is what's going to give me my angle a.
01:34
So inverse cosine.
01:37
We got 12 squared.
01:40
Plus 51 squared minus 48 squared divided by 2 times 12 times 51.
01:51
Okay.
01:52
And that comes out to an angle a is going to be 68.
01:59
Once one decimal place, so 68 .9 degrees.
02:07
From there, i can now set up a law of signs.
02:11
So i will do that with, sorry, let's say your angle a is here...