Special right triangle is 90°, leaving the remaining angle to be 30°. Right triangles whose sides are of integer lengths, with the sides collectively known as Pythagorean triples, possess angles that cannot all be rational numbers of degrees. (This follows from Niven's theorem.) They are most useful in that they may be easily remembered and any multiple of the sides produces the same relationship. Using Euclid's formula for generating Pythagorean triples, the sides must be in the ratio where "m" and "n" are any positive integers such that . There are several Pythagorean triples which are well-known, including those with sides in the
Schwarz triangle function of the upper half plane. To see how to handle the case when an angle of Δ is a right angle, note that the inequality implies that if one of the angles is a right angle, say "a" = 2, then both "b" and "c" are greater than 2 and one of them, "b" say, must be greater than 3. In this case, reflecting the triangle across the side AB gives an isosceles hyperbolic triangle with angles /"c", /"c" and 2/"b". If 2/"b" ≤ /3, i.e. "b" is greater than 5, then all the angles of the doubled triangle are