Question

What is the value of b in this diagram?

Answer 1

The Law of Sines looks like this:

b a

------- = --------

sin B sin A

Here we know the values of a, A and B:

b 7.89

--------- = -------------

sin 40 sin 121.5

7.89*sin 40 deg

Cross-multiplying, we get b = -------------------------

sin 121.5 deg

Answer 2

Apparently, you are to make use of the law of sines. It tells you

b/sin(B) = a/sin(A)

You can multiply by sin(B) to find b.

b = sin(B)·a/sin(A)

Substituting given values, this becomes

b = sin(40°)·7.89/sin(121.5°)

b ≈ 5.95