Law of cosines
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°.
- 9² + 9² = 162, and cos 70° ≈ 0.342, so 2·9·9·cos 70° ≈ 55.41. That leaves c² ≈ 106.59; take the square root: 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
9² + 9² = 162, and cos 70° ≈ 0.342, so 2·9·9·cos 70° ≈ 55.41. That leaves c² ≈ 106.59; take the square root: c ≈ 10.3.