What is the law of cosines?

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The law of cosines, also known as the cosine formula or cosine rule, is a generalization of the Pythagorean theorem. It relates the lengths of the sides of any triangle: $c^{2} = a^{2} + b^{2} - 2 a b c o s C$ , where C is the angle opposite side c. When two sides and the angle between them (SAS) or all three sides (SSS) are known, the law of cosines can be used to find an unknown side or angle, respectively, in these cases.