Hyperbolic law of cosines - 2nd law

Description

In hyperbolic geometry, the law of cosines is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar law of cosines from plane trigonometry, or the spherical law of cosines in spherical trigonometry.

Take a hyperbolic plane whose Gaussian curvature is -1/k^2 . Then given a hyperbolic triangle ABC with angles α, β, γ, and side lengths BC = a, AC = b, and AB = c, two rules hold the second of which is shown here.

Related formulas

Variables

αangle (dimensionless)
βangle (dimensionless)
γangle (dimensionless)
alength (dimensionless)
kcarvature (dimensionless)