Law of Cosines Calculator
Use the law of cosines to find a third side from two sides and their included angle.
How to use
- Enter positive side lengths a and b.
- Enter included angle C strictly between 0° and 180°.
Capabilities and scope
After validating the triangle, the runner also reports area and perimeter.
How it works
It uses c=√(a²+b²−2ab cos C); area is ab sin C/2.
Example
a=3, b=4, C=90° give c=5 and area 6.
Useful for
- Solve a triangle from SAS information
- Extend the Pythagorean relationship to non-right angles
Before you use it
- Angle is in degrees, and degenerate 0° or 180° cases are rejected.
Frequently asked questions
Does 90° match Pythagorean theorem?
Yes. cos90°=0, reducing the equation to a²+b²=c².