Law of Cosines Calculator
c² = a² + b² − 2ab·cos(C). Solve any triangle given SAS or SSS.
Result
Side c
7.211103
c² = 8² + 6² − 2(8)(6)cos(60°) = 52.0000.
- Side a8
- Side b6
- Angle C60°
- Side c7.211103
- Angle A73.8979°
- Angle B46.1021°
- Area½ab sin C20.784610
Step-by-step
- c² = a² + b² − 2ab cos C = 64 + 36 − 48.0000 = 52.0000.
- c = √52.0000 = 7.2111.
- A = arccos((b² + c² − a²) / 2bc) = 73.8979°.
- B = 180° − A − C = 46.1021°.
How to use this calculator
- Enter two sides and the included angle (SAS).
- Read third side and other angles.
About this calculator
Law of cosines: c² = a² + b² − 2ab·cos(C). Generalizes Pythagorean theorem (when C = 90°, cos C = 0, giving c² = a² + b²). Used to solve SAS triangles (two sides + included angle) or SSS (three sides — solve for any angle: cos(A) = (b² + c² − a²)/(2bc)). Also gives triangle area via ½ab·sin(C).
Frequently asked
When C = 90°, cos(C) = 0, so c² = a² + b² (the Pythagorean theorem).
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