Hypotenuse formula_9 One may also obtain the value of the angle formula_9 by the equation: in which formula_16 is the other cathetus. 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
Automedian triangle much more recent. The problem of characterizing automedian triangles was posed in the late 19th century in the "Educational Times" (in French) by Joseph Jean Baptiste Neuberg, and solved there with the formula 2"a" = "b" + "c" by William John Greenstreet. Apart from the trivial cases of equilateral triangles, the triangle with side lengths 17, 13, and 7 is the smallest (by area or perimeter) automedian triangle with integer side lengths. There is only one automedian right triangle, the triangle with side lengths proportional to 1, , and . This triangle is the second triangle in the spiral of