CalcTool: Triangle from three sides calculator

MyCT
Main
Forum

Triangle from three sides

Angles and area from all side lengths.

Mathematics index
Geometry (2d) index

$Triangle from three sides diagram$

The three angles of a triangle are calculated from side lengths by cutting it into two right-angled triangles and solving Pythagoras' theorem for each one. These simultaneous equations give the upright length, thus the angles can be found by trigonometry, and the area follows.

This calc may be used as part of a solution to many other geometric problems. Other calcs are available to give triangle properties from two sides and one angle, and from one side and two angles. Three angles alone does not allow calculation of side lengths, although the ratios of their lengths can be found