A spherical triangle has interior angles equal to 168degrees, 103degrees and 92degrees. Compute the sides of the spherical triangle.

side a = ______ degrees

side b = _______ degrees

side c = _______ degrees

in Geometry Answers by Level 1 User (380 points)

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From Wikipedia. First convert all angles to radians by multiplying by π/180, then apply the formula for sin½a.

I got sin½a=0.9991, so ½a=1.5285 radians, and a=3.0570 (175.15°).

Use the spherical sine rule to find the other angles. a/sinA=b/sinB, so b=asinB/sinA=14.3267 radians (820.86°, adjusted by subtracting 720°=100.86°). a/sinA=c/sinC, c=asinC/sinA=14.6945 (841.94°, adjusted by subtracting 720°=121.94°). The adjustment is to get the angles to be between 0° and 360°. The angles appear to be a=175.15°, b=100.86°, c=121.94°.

by Top Rated User (761k points)

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