Identities
Spherical triangles satisfy a spherical law of cosines
The identity may be derived by considering the triangles formed by the tangent lines to the spherical triangle subtending angle C and using the plane law of cosines. Moreover, it reduces to the plane law in the small area limit.
A variation on the law of cosines, the second spherical law of cosines, (also called the cosine rule for angles ) states:
They also satisfy an analogue of the law of sines
Spherical triangles satisfy the half-side formula :
where .
Read more about this topic: Spherical Trigonometry