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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)}.
\end{displaymath} (1)

The angle $C$ is given in terms of $A$ and $B$ by
\end{displaymath} (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}
\end{displaymath} (3)

to obtain
$\displaystyle a$ $\textstyle =$ $\displaystyle {\sin A\over\sin(\pi-A-B)}c$ (4)
$\displaystyle b$ $\textstyle =$ $\displaystyle {\sin B\over\sin(\pi-A-B)}c.$ (5)

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

© 1996-9 Eric W. Weisstein