Special right triangle than 256: Isosceles right-angled triangles cannot have sides with integer values, because the ratio of the hypotenuse to either other side is , but cannot be expressed as a ratio of two integers. However, infinitely many "almost-isosceles" right triangles do exist. These are right-angled triangles with integral sides for which the lengths of the non-hypotenuse edges differ by one. Such almost-isosceles right-angled triangles can be obtained recursively, "a" is length of hypotenuse, "n" = 1, 2, 3, ... Equivalently, where {"x", "y"} are the solutions to the Pell equation , with the hypotenuse "y" being the odd terms of the
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