Hypotenuse Hypotenuse In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite of the right angle. The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides. For example, if one of the other sides has a length of 3 (when squared, 9) and the other has a length of 4 (when squared, 16), then their squares add up to 25. The length of the hypotenuse
Special right triangle its sides be in a geometric progression. The 3–4–5 triangle is the unique right triangle (up to scaling) whose sides are in an arithmetic progression. Let be the side length of a regular decagon inscribed in the unit circle, where "φ" is the golden ratio. Let be the side length of a regular hexagon in the unit circle, and let {2}}</math>}} be the side length of a regular pentagon in the unit circle. Then , so these three lengths form the sides of a right triangle. The same triangle forms half of a golden rectangle. It may also be found