In triangle ABC, what is the measure of angle C if A = 120°, a = 25, and b = 24?

Using the Law of Sines we have :

(Sin B / 24) = (Sin 120 / 25)   .......     SinB = (24*sin120/25)

So, using the sine inverse to find B

Sin^-1 (24*sin120/25) ≈ 56.24 degrees

So C= (180 - 56.24 - 120) = 3.76 degrees