Law of Sines and Law of Cosines

Any triangle

Law of sines

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2 R

R the circumradius

Law of cosines

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

Angle from three sides

\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b}

Area from two sides and the angle between

A = \frac{1}{2} a b \sin C

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