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

The measure of ∠B is 18.9°

Explanation:

Given triangle ABC in which

∠A = 120°, a = 8, and b = 3

we have to find ∠B

By sine law,

`(\sin \angle A)/(a)=(\sin \angle B)/(b)=(\sin \angle C)/(c)`

`(\sin \angle A)/(a)=(\sin \angle B)/(b)`

`(\sin 120^(\circ))/(8)=(\sin \angle B)/(3)`

`\sin \angle B=3(\sin 120^(\circ))/(8)=(3)/(16)\sqrt3`

`\angle B=sin^(-1)((3)/(16)\sqrt3)=18.951\sim 18.9^(\circ)`

The measure of ∠B is 18.9°