Integer triangle rational formula_14 where formula_15 reduces the generated Heronian triangle to its primitive and formula_16 scales up this primitive to the required size. A Pythagorean triangle is right angled and Heronian. Its three integer sides are known as a Pythagorean triple or Pythagorean triplet or Pythagorean triad. All Pythagorean triples formula_17 with hypotenuse formula_18 which are primitive (the sides having no common factor) can be generated by where "m" and "n" are coprime integers and one of them is even with "m" > "n". Every even number greater than 2 can be the leg of a Pythagorean triangle (not necessarily primitive)
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