# 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

a | side length (dimensionless) |

k | curvature (dimensionless) |

b | side length (dimensionless) |

c | side length (dimensionless) |

α | angle (dimensionless) |