Law of Cosines

High School

Definition

The Law of Cosines relates one side of a triangle to the other two sides and their included angle. It generalizes the Pythagorean theorem.

c² = a² + b² - 2abcos C

Law of Cosines

cos C = (a² + b² - c²)/(2ab)

Law of Cosines (for finding angles)

Example 1

Find c when a = 5, b = 7, and C = 60°.

Discovered by: Ancient Greek mathematicians

Appeared in geometric form in Euclid's Elements; the modern formula developed with trigonometry.