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
Special right triangle allows one to quickly calculate various lengths in geometric problems without resorting to more advanced methods. "Angle-based" special right triangles are specified by the relationships of the angles of which the triangle is composed. The angles of these triangles are such that the larger (right) angle, which is 90 degrees or radians, is equal to the sum of the other two angles. The side lengths are generally deduced from the basis of the unit circle or other geometric methods. This approach may be used to rapidly reproduce the values of trigonometric functions for the angles 30°, 45°, and 60°. Special