Law of cosines
Property of all triangles on a Euclidean plane / From Wikipedia, the free encyclopedia
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This article is about the trigonometric identity. For the cosine law of optics, see Lambert's cosine law.
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. For a triangle with sides and opposite respective angles and (see Fig. 1), the law of cosines states:
The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if is a right angle then and the law of cosines reduces to
The law of cosines is useful for solving a triangle when all three sides or two sides and their included angle are given.