- #1

- 12

- 0

## Homework Statement

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.

## Homework Equations

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.