law of cosines

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law of cosines

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law of cosines (uncountable)

1. (trigonometry) A generalization of the Pythagorean theorem that relates the lengths of the sides of a triangle to the cosine of one of its angles.

Let a, b, and c be the lengths of the sides of a triangle opposite angles A, B, and C. The law of cosines states

${\displaystyle a^{2}=b^{2}+c^{2}-2bc\cos {A}}$

${\displaystyle b^{2}=a^{2}+c^{2}-2ac\cos {B}}$

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

• cosine formula
• cosine law
• cosine rule

• law of sines