Special right triangle than 256: Isosceles right-angled triangles cannot have sides with integer values, because the ratio of the hypotenuse to either other side is , but cannot be expressed as a ratio of two integers. However, infinitely many "almost-isosceles" right triangles do exist. These are right-angled triangles with integral sides for which the lengths of the non-hypotenuse edges differ by one. Such almost-isosceles right-angled triangles can be obtained recursively, "a" is length of hypotenuse, "n" = 1, 2, 3, ... Equivalently, where {"x", "y"} are the solutions to the Pell equation , with the hypotenuse "y" being the odd terms of the
Altitude (triangle) (not extended). In an obtuse triangle (one with an obtuse angle), the foot of the altitude to the obtuse-angled vertex falls in the interior of the opposite side, but the feet of the altitudes to the acute-angled vertices fall on the opposite extended side, exterior to the triangle. This is illustrated in the adjacent diagram: in this obtuse triangle, an altitude dropped perpendicularly from the top vertex, which has an acute angle, intersects the extended horizontal side outside the triangle. The three (possibly extended) altitudes intersect in a single point, called the orthocenter of the triangle, usually denoted by .