Law of sines, step by step

When a triangle has two angles and a side opposite one of them, the law of sines finds the rest: a/sin A = b/sin B.

The question

In △ABC, a = 6, ∠A = 60°, ∠B = 45°. Find b:

Find b by the law of sines

b=a · sin B / sin A

b=6 · sin 45° / sin 60°

b≈4.9

Two angles and the side opposite one — that is the law of sines: a/sin A = b/sin B.
Substitute a = 6, A = 60°, B = 45°.
Evaluate and round to one place: b ≈ 4.9.

How it works.

01
Two angles and the side opposite one — that is the law of sines: a/sin A = b/sin B.
02
Substitute a = 6, A = 60°, B = 45°.
03
Evaluate and round to one place: b ≈ 4.9.