Question

a. If a spherical Triangle on Earth has an excess of 30 degrees, find the area of this spherical triangle measured in square miles.
b. If a spherical triangle on the moon has an excess of 30 degrees, find the area of this spherical triangle in sqare miles.
c. Find the ratio of the above answers to a and b.

Answer 1

The area of a spherical triangle bounded by arcs of three great circles is defined by A = Pi(r^2)E/180 where r = the spherical radius and E = the spherical excess, defined by E = (A+B+C)-180, A, B and C being the three spherical angles of the sphere.