Solve the triangle round your answers to two decimal places...

Solve the triangle. (Round your answers to two decimal places.) A=43deg ,B=59deg ,a=19 C= ◻ ○ b= ◻ c= ◻ Solve the triangle. (Round your answers to two decimal places.) A=43B=59a=19 C= b= =J

Transcript

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.