Enter the length of any side to calculate the length of the other 2
In plane geometry, constructing the diagonal of a square results in a triangle whose three angles are in the
ratio 1 : 1 : 2, adding up to 180° or π radians. Hence, the angles respectively measure 45° (π/4), 45°
(π/4), and 90° (π/2). The sides in this triangle are in the ratio 1 : 1 : √2, 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 √2/2 and the greatest ratio of the altitude from the hypotenuse to the sum of the legs,
namely √2/4.
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.