What is the sum of the angles of a spherical triangle formed on the surface of a sphere of radius R? The triangle is formed by the intersections of the arcs of great circles. Let
A be the area of the surface of the sphere enclosed by the triangle.
This question is a result of self-study.
The text I have provides the following formula: sum of the angles = π + A/R^2
The Attempt at a Solution
A course I had last year covered steradians. My confusion relates to the formula. If the triangle was two-dimensional, the sum of the angles would of course be π radians. Also, the surface area enclosed by the spherical triangle subtends a solid angle of A/R^2 steradians.
Do these details mean that the right side of the formula listed above is a sum of radians and steradians? Are radians and steradians both just considered “degrees” that can be added together?
Thank you for clarifying.