[math-fun] Spherical geometry puzzle

I recently searched in vain for an expression for the area of a spherical triangle in terms of its *sides* having lengths a, b, c. (Assume that the triangle is drawn on the surface of a sphere of radius = 1, with sides that are arcs of great circles, and whose angles are all < π radians.) So I figured out my own formula, which definitely took a few minutes. Puzzle: Find such a formula without consulting any references. —Dan