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ASA Theorem


ASATheorem

Specifying two adjacent angles A and B and the side between them c uniquely (up to geometric congruence) determines a triangle with area

 K=(c^2)/(2(cotA+cotB)).
(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/(sinA)=b/(sinB)=c/(sinC)
(3)

to obtain

a=(sinA)/(sin(pi-A-B))c
(4)
b=(sinB)/(sin(pi-A-B))c.
(5)

See also

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

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Cite this as:

Weisstein, Eric W. "ASA Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ASATheorem.html

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