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
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