Law of Cosines Calculator
Use the law of cosines to find the third side of a triangle given two sides and the included angle.
deg
Side C
8.8882
Angle A43.00 deg
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
Example Calculation
Find side c: a = 7, b = 10, angle C = 60°.
- 01c² = 49 + 100 - 2(7)(10)cos(60°)
- 02= 149 - 140 × 0.5
- 03= 149 - 70 = 79
- 04c = √79 ≈ 8.8882
Frequently Asked Questions
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