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AAS Theorem


AASTheorem

Specifying two angles A and B and a side a opposite A uniquely determines a triangle with area

K=(a^2sinBsinC)/(2sinA)
(1)
=(a^2sinBsin(pi-A-B))/(2sinA).
(2)

The third angle is given by

 C=pi-A-B,
(3)

since the sum of angles of a triangle is 180 degrees (pi radians). Solving the law of sines

 a/(sinA)=b/(sinB)
(4)

for b gives

 b=a(sinB)/(sinA).
(5)

Finally,

c=bcosA+acosB
(6)
=a(sinBcotA+cosB)
(7)
=asinB(cotA+cotB).
(8)

See also

AAA Theorem, ASA Theorem, ASS Theorem, SAS Theorem, SSS Theorem, Triangle

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Cite this as:

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

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