Law of cosines

Generalization of Pythagorean theorem

In trigonometry, the law of cosines (also known as the cosine formula or cosine rule or Al-Kashi’s theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides ⁠ a {\displaystyle a} ⁠, ⁠ b {\displaystyle b} ⁠, and ⁠ c {\displaystyle c} ⁠, opposite respective angles ⁠ α {\displaystyle \alpha } ⁠, ⁠ β {\displaystyle \beta } ⁠, and ⁠ γ {\displaystyle \gamma } ⁠ (see Fig. 1), the law of cosines states: c 2 = a 2 + b 2 − 2 a b cos ⁡ γ , a 2 = b 2 + c 2 − 2 b c cos ⁡ α , b 2 = a 2 + c 2 − 2 a c cos ⁡ β .

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