Law of sines

See Sine rule for a proof.

In geometry the law of sines (also known as sine rule) is useful for calculating one side or angle of any triangle, when five of the six angles and sides are known. It can be stated as

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

where the lengths $a$, $b$, and $c$ correspond to the sides opposite the respective angles $A$, $B$, and $C$ as shown in the image.

Triangle