Spherical Law of Cosines

Theorem
Let $\triangle ABC$ be a spherical triangle on the surface of a sphere whose center is $O$.

Let the sides $a, b, c$ of $\triangle ABC$ be measured by the angles subtended at $O$, where $a, b, c$ are opposite $A, B, C$ respectively.

Then:

Also known as
This result is also known as the Spherical Law of Cosines.

Historical Note
This result was first stated by in his De Triangulis Omnimodus of 1464.