Calxsolver
Trigonometry

Law of Cosines

The law of cosines, c² = a² + b² − 2ab·cos C, generalises the Pythagorean theorem to any triangle. Given two sides and the angle between them, this solver finds the third side, then uses the law of cosines again to find the remaining angles.

Law of Cosines

Solve a triangle from two sides and the included angle.

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Frequently asked questions

What is the SAS case?

SAS means Side-Angle-Side: you know two sides and the angle included between them. The law of cosines solves it directly.

How is it related to the Pythagorean theorem?

When the included angle is 90°, cos C = 0 and the formula reduces to c² = a² + b².

Can the included angle be obtuse?

Yes. Any angle strictly between 0° and 180° is valid; an obtuse angle simply gives a longer third side.

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