Law of sines

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°.
On a calculator, in degrees: sin 45° ≈ 0.7071 and sin 60° ≈ 0.866. 6 × 0.7071 ÷ 0.866 ≈ 4.90, so b ≈ 4.9 to one place.

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
On a calculator, in degrees: sin 45° ≈ 0.7071 and sin 60° ≈ 0.866. 6 × 0.7071 ÷ 0.866 ≈ 4.90, so b ≈ 4.9 to one place.