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
Acute and obtuse triangles according to This implies that the longest side in an obtuse triangle is the one opposite the obtuse-angled vertex. An acute triangle has three inscribed squares, each with one side coinciding with part of a side of the triangle and with the square's other two vertices on the remaining two sides of the triangle. (In a right triangle two of these are merged into the same square, so there are only two distinct inscribed squares.) However, an obtuse triangle has only one inscribed square, one of whose sides coincides with part of the longest side of the triangle. All triangles