SOLUTION: Find the area of a spherical triangle ABC whose angles are 93 degrees, 64 degrees and 116 degrees. The radius of the sphere is 100 m. Please explain.

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Question 1117512: Find the area of a spherical triangle ABC whose angles are 93 degrees, 64 degrees and 116 degrees. The radius of the sphere is 100 m. Please explain.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Using Girard's theorem,
A=alpha%2Bbeta%2Bgamma-pi
alpha=%28%282pi%29%2F360%29%2A93=%2831%2F60%29pi
beta=%28%282pi%29%2F360%29%2A64=%2816%2F45%29pi
gamma=%28%282pi%29%2F360%29%2A116=%2829%2F45%29pi
So,
A%2Fpi=31%2F60%2B16%2F45%2B29%2F45-1
A%2Fpi=31%2F60
A=%2831%2F60%29pi
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.
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For definition on why it works, look up Girard's theorem spherical triangles.