ASA Theorem

Specifying two adjacent Angles $A$ and $B$ and the side between them $c$ uniquely determines a Triangle with Area

$$K={c^2\over 2(\cot A+\cot B)}.$$ (1)

The angle $C$ is given in terms of $A$ and $B$ by

$$C=\pi-A-B,$$ (2)

and the sides $a$ and $b$ can be determined by using the Law of Sines

$${a\over\sin A}={b\over\sin B}={c\over\sin C}$$ (3)

to obtain

$$a = {\sin A\over\sin(\pi-A-B)}c$$ (4)

$$b = {\sin B\over\sin(\pi-A-B)}c.$$ (5)

See also AAA Theorem, AAS Theorem, ASS Theorem, SAS Theorem, SSS Theorem, Triangle