# Law of cotangents (in term of tangents)

## Description

In trigonometry, the law of cotangents is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles. The cotangent of a half-angle equals the ratio of the semi-perimeter minus the opposite side to the said angle, to the inradius for the triangle. Using the term of tangent: “the tangent of a half-angle equals the ratio of the inradius for the triangle to the semi-perimeter minus the opposite side to the said angle”.

Related formulas## Variables

A | Angle less than 180° (degree) |

r_{in} | The radius of the inscribed circle for the triangle (m) |

s | The semi-perimeter for the triangle (m) |

a | The opposite side to angle A (m) |