# Spherical Law of Cosines

Spherical Law of Cosines

Draw a spherical triangle on the surface of the unit sphere with center at the origin . Let the sides (arcs) opposite the vertices have lengths , and , and let be the angle at vertex . The spherical law of cosines is then given by , with two analogs obtained by permutations.

ABC

O

a

b

c

A

A

cosa=cosbcosc+sinbsinccosA