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Law of Sines and Cosines


Law of Sines

A blue equilateral triangle on a white background, with vertices labeled A, B, and C and sides labeled a, b, and c.
sin A a  =  sin B b  =  sin C c

Law of Cosines

For this (or any given triangle), the Law of Cosines says:
c2 = a2 + b2 − 2ab cos C

A blue triangle with labeled vertices A, B, and C; sides are labeled a, b, and c.

This law is helpful if you need to find the angles of a triangle but know all the side lengths, or if you want to solve for the third side of a triangle when you know the lengths of the other two sides and the angle between them.

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