Special right triangle triangles are used to aid in calculating common trigonometric functions, as below: The 45°–45°–90° triangle, the 30°–60°–90° triangle, and the equilateral/equiangular (60°–60°–60°) triangle are the three Möbius triangles in the plane, meaning that they tessellate the plane via reflections in their sides; see Triangle group. In plane geometry, constructing the diagonal of a square results in a triangle whose three angles are in the ratio 1 : 1 : 2, adding up to 180° or radians. Hence, the angles respectively measure 45° (), 45° (), and 90° (). The sides in this triangle are in the ratio 1 : 1
Right triangle legs can be expressed in terms of the inradius and the other leg as A triangle "ABC" with sides formula_13, semiperimeter "s", area "T", altitude "h" opposite the longest side, circumradius "R", inradius "r", exradii "r", "r", "r" (tangent to "a", "b", "c" respectively), and medians "m", "m", "m" is a right triangle if and only if any one of the statements in the following six categories is true. All of them are of course also properties of a right triangle, since characterizations are equivalences. The trigonometric functions for acute angles can be defined as ratios of the sides of