Question

Find the measure of angle C. Round your answer to the nearest hundredth.

Answer 1

We need to use the law of sines to solve for the triangle. Do you know what that is?

Answer 2

I do know. I was unsure of where to start with this problem, though. Wouldn't I need to use the law of cosines first since there aren't enough angle measurements in the triangle?

Answer 3

Oh yes, I thought we needed to use the law of cosine and then I thought against it. Yes we do. lol.

Answer 4

We need to use this cosine formula to get the value of the side b so we can move forward with it :)

So here is the formula:

\(\sf b^2= a^2+c^2-2ac\times cos(B)\)

Answer 5

And then after calculating the side length of b, we can use the law of sin to figure out the angle of c. :)

Answer 6

So...it would be...
b^2=(19)^2+(15)^2-2(19)(15)cos(120)

Which simplifies to...
b^2=361+225-570cos(120)
=871

Does this look right so far? :)

Answer 7

b=29.5

Answer 8

Correct! :D

Answer 9

And now we use the Law of Sin formula so:

\(\sf\Large\frac{sin \beta}{B}=\frac{sin\gamma}{C}\)

And plugging in the numbers we get:

\(\sf\Large\frac{sin(120)}{29.5}=\frac{sinc}{15}\)

Answer 10

And we will need to first isolate \(\sf sinc\) and then use \(\sf sin^{-1}\) to calculate for the angle \(\sf c\)

Answer 11

Do it all the calculator work all at once so you don't simplify earlier and at the end get a wrong answer.

Answer 12

At what point do I use sin^-1?

Answer 13

At the end. First isolate sin(c) and then you use sin^-1 to get c alone.

Answer 14

So until then, it would be
29.5sinC=13

Answer 15

sinC=.44
Then sin^-1(.44)
=26.11

Answer 16

Thank you!! You've been a great help!! :D

Answer 17

The final answer would be 26.13

Because if you plug in this in you your calculator

\(\sf\Large sin^{-1}(\frac{sin(120)\times 15}{29.5}) = 26.13\)

You rounded off a little early.

But thank you for actually participating! :)