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 Geometry and Trigonometry
 Law of Sines SSA [Two Solutions Case], Help needed
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Meshu
New Member

Canada
2 Posts

Posted - 10/23/2007 :  18:51:19  Show Profile  Reply with Quote

Hey guys,

Actually I have a problem in determining if an SSA triangle has one solution or two ... Does anyone know how to know that by looking at the given information?

An example question,

Solve triangle ABC if A=43.1, a=186.2 and b=248.6


Thanks in advance
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skeeter
Advanced Member

USA
5634 Posts

Posted - 10/23/2007 :  19:19:07  Show Profile  Reply with Quote
use the law of sines and solve for sin(B) ...

sin(B) = b*sin(A)/a = 0.91225...

if sin(B) = 0.91225... , then angle B has two possible values, namely sin-1(.91225...) = 65.8 degrees and 180-65.8 = 114.2 degrees.

both angles will work since mA + mB < 180 degrees for both values of B.

If you run into a situation where mA + mB 180, then that angle value for B will not work, and you only get one possible triangle.

A third possibility exists ... if sin(B) works out to be > 1, then no triangle possible.
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Meshu
New Member

Canada
2 Posts

Posted - 10/24/2007 :  20:56:59  Show Profile  Reply with Quote

Many thanks for the information. It was very helpful and I think i understood it now ..
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