Question

Round your answer to this problem to the nearest degree.
In triangle ABC, if ∠A = 120°, a = 8, and b = 3, then ∠B =

Answer 1

Angle B = 45 because 8:120 and 3:45 are equivalent proportions

Answer 2

Answer:

The measure of ∠B is 18.9°    

Step-by-step explanation:

Given triangle ABC in which  

∠A = 120°, a = 8, and b = 3

we have to find ∠B

By sine law,

$\frac{\sin \angle A}{a}=\frac{\sin \angle B}{b}=\frac{\sin \angle C}{c}$

$\frac{\sin \angle A}{a}=\frac{\sin \angle B}{b}$

$\frac{\sin 120^{\circ}}{8}=\frac{\sin \angle B}{3}$

$\sin \angle B=3\frac{\sin 120^{\circ}}{8}=\frac{3}{16}\sqrt3$

$\angle B=sin^{-1}(\frac{3}{16}\sqrt3)=18.951\sim 18.9^{\circ}$

The measure of ∠B is 18.9°