Law of cosines, step by step

When a triangle gives two sides and the angle between them, the law of cosines finds the third side.

The question

In △ABC, a = 9, b = 9, ∠C = 70°. Find c:

Find c by the law of cosines

c²=a² + b² − 2ab·cos C

c²=9² + 9² − 2·9·9·cos 70°

c≈10.3

Two sides and the angle between them — that is the law of cosines: c² = a² + b² − 2ab·cos C.
Substitute a = 9, b = 9, C = 70°.
Take the square root and round: c ≈ 10.3.

How it works.

01
Two sides and the angle between them — that is the law of cosines: c² = a² + b² − 2ab·cos C.
02
Substitute a = 9, b = 9, C = 70°.
03
Take the square root and round: c ≈ 10.3.