Quick Math‎ > ‎

Spherical Excess

If the interior angles of a spherical triangle add up to 252 degrees, what fraction of the sphere's surface is inside the triangle?

Answer: 1/10th

The spherical excess is the sum of the interior angles in excess of 180 degrees.  (E=252 -180= 72deg)

The ratio of the spherical excess to 720 degrees is equal to the ratio of the area of the triangle to the area of the sphere.

triangle area/sphere area = 72/720= 1/10.