The law of cosines relates the angles of a triangle to the length of the sides: c2 = a2 + b2 - 2ab cosγ.. The law of cosines is a generalization of the pythagorean theorem. Since cos(90°) is zero, the formula is c2 = a2 + b2 for right triangles.
A geometric equivalent of the law of cosines was described in Euclid's Elements, Book 2, proposition 12 and proposition 13. The law of cosines can also be used to generate the formula for the angle opposite side c, if one knows the lengths of the sides:
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