Math

Law of Cosines Calculator

Find the third side of a triangle from two sides and the included angle.

Calculated Output

Side c 6.245

Formula: c² = a² + b² − 2ab·cos(C)

Step-by-Step Breakdown

1. Values used:

2. Side a = 5

3. Side b = 7

4. Included angle C = 60 degrees

6. Side c = 6.245

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The math behind it

c² = a² + b² − 2ab·cos(C). At C = 90° it reduces to the Pythagorean theorem.

a 5, b 7, C 60° → c = 6.24.

Find an angle?

Rearrange to cos(C) = (a² + b² − c²) ÷ 2ab.