Hyperbolic law of cosines - 1st 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/k2 . 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 first of which is shown here.

Related formulas

Variables

aside length (dimensionless)
kcurvature (dimensionless)
bside length (dimensionless)
cside length (dimensionless)
αangle (dimensionless)