Law of Cosines Calculator — Formel
## Law of Cosines
### Formula
**c² = a² + b² - 2ab × cos(C)**
**c = sqrt(a² + b² - 2ab × cos(C))**
This generalizes the Pythagorean theorem. When C = 90°, cos(C) = 0, and it reduces to c² = a² + b².
### When to Use
- You know two sides and the included angle (SAS) and want the third side
- You know all three sides (SSS) and want an angle
### Formula
**c² = a² + b² - 2ab × cos(C)**
**c = sqrt(a² + b² - 2ab × cos(C))**
This generalizes the Pythagorean theorem. When C = 90°, cos(C) = 0, and it reduces to c² = a² + b².
### When to Use
- You know two sides and the included angle (SAS) and want the third side
- You know all three sides (SSS) and want an angle
Lösungsbeispiel
Find side c: a = 7, b = 10, angle C = 60°.
- c² = 49 + 100 - 2(7)(10)cos(60°)
- = 149 - 140 × 0.5
- = 149 - 70 = 79
- c = √79 ≈ 8.8882