Special right triangle : , which follows immediately from the Pythagorean theorem. Of all right triangles, the 45°–45°–90° degree triangle has the smallest ratio of the hypotenuse to the sum of the legs, namely . Of all right triangles, the 45°–45°–90° degree triangle has the greatest ratio of the altitude from the hypotenuse to the sum of the legs, namely . Triangles with these angles are the only possible right triangles that are also isosceles triangles in Euclidean geometry. However, in spherical geometry and hyperbolic geometry, there are infinitely many different shapes of right isosceles triangles. This is a triangle whose three angles
Hyperbolic triangle In other words, the quantity in the paragraph above is supposed to be equal to 1. Trigonometric formulas for hyperbolic triangles depend on the hyperbolic functions sinh, cosh, and tanh. If "C" is a right angle then: We also have the following equations: The area of a right angled triangle is: also The instance of an omega triangle with a right angle provides the configuration to examine the angle of parallelism in the triangle. In this case angle "B" = 0, a = c = formula_18 and formula_19, resulting in formula_20. The trigonometry formulas of right triangles also give the