Question

Find the measure of b, given m∠A = 38°, m∠B = 74°, and a = 31.

Answer 1

b = 48.4

Using the Law of Sines, we have


`(sin(A))/(a)=(sin(B))/(b) \\ \\ (sin(38))/(31)=(sin(74))/(b)`

Cross multiplying gives us
b sin 38 = 31(sin 74)

Dividing both sides by sin 38 we have:
(b sin 38)/(sin 38) = 31(sin 74)/(sin 38)
b = 48.4