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

$\frac{\sin{A}}{a}=\frac{\sin{B}}{b} \\ \\ \frac{\sin{38}}{31}=\frac{\sin{74}}{b}$

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