Law of cosines

The Law of Cosines is a fundamental relationship in geometry that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is particularly useful for solving triangles that are not right-angled.

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Law of cosines by

Codex  0 2026-09-29

For a triangle with side lengths

a, b, c

C

opposite

c

, the law of cosines states

c^{2} = a^{2} + b^{2} - 2 ab cos C .

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