### Find the word definition

##### Wiktionary
law of cosines

n. (context trigonometry English) A statement that relates the lengths of the side of a triangle to the cosine of one of its angle.

##### Wikipedia
Law of cosines

In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. Using notation as in Fig. 1, the law of cosines states

c = a + b − 2abcosγ,
where denotes the angle contained between sides of lengths and and opposite the side of length .

The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if the angle is a right angle (of measure 90 °, or radians), then , and thus the law of cosines reduces to the Pythagorean theorem:

c = a + b.

The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known.

By changing which sides of the triangle play the roles of , , and in the original formula, the following two formulas also state the law of cosines:

a = b + c − 2bccosα,

b = a + c − 2accosβ.