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
Altitude (triangle) the tangential triangle, and the center of similitude of the orthic and tangential triangles, are on the Euler line. Trilinear coordinates for the vertices of the tangential triangle are given by For more information on the orthic triangle, see here. For any triangle with sides and semiperimeter , the altitude from side is given by This follows from combining Heron's formula for the area of a triangle in terms of the sides with the area formula (1/2)×base×height, where the base is taken as side and the height is the altitude from . Consider an arbitrary triangle with sides and with