Hyperbolic law of cosines

For opposite side $a$, $\cosh a=(\cos \alpha +\cos \beta \cos \gamma )/(\sin \beta \sin \gamma )$.

A hyperbolic triangle is determined up to isometry by its three angles. Indeed, the angle form of the hyperbolic law of cosines determines every side length from the angles, after which hyperbolic side-side-side congruence determines the triangle. This differs from Euclidean geometry because hyperbolic space has an intrinsic length scale.