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
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
