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