Spherical trigonometry

Summary

Spherical trigonometry studies the relations between the sides and the angles of spherical triangles, the triangles on a sphere bounded by arcs of great circles. Its main formulas are the spherical law of cosines, $\cos c = \cos a \cos b + \sin a \sin b \cos \gamma$, and the spherical law of sines, $\sin a / \sin \alpha = \sin b / \sin \beta = \sin c / \sin \gamma$. It is the part of spherical geometry used in astronomy, geodesy and navigation. The area of a spherical triangle is given by Girard's theorem.