Trigonometric constants expressed in real radicals in a regular polygon: a vertex, an edge center containing that vertex, and the polygon center. An "n"-gon can be divided into 2"n" right triangles with angles of , 90 − , 90} degrees, for "n" in 3, 4, 5, … Constructibility of 3, 4, 5, and 15-sided polygons are the basis, and angle bisectors allow multiples of two to also be derived. In degree format, sin and cos of 0, 30, 45, 60, and 90 can be calculated from their right angled triangles, using the Pythagorean theorem. In radian format, sin and cos of / 2 can be expressed
Special right triangle within a regular icosahedron of side length "c": the shortest line segment from any vertex "V" to the plane of its five neighbors has length "a", and the endpoints of this line segment together with any of the neighbors of "V" form the vertices of a right triangle with sides "a", "b", and "c". Special right triangle A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called