Right triangle Right triangle A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the "hypotenuse" (side "c" in the figure). The sides adjacent to the right angle are called "legs" (or "catheti", singular: "cathetus"). Side "a" may be identified as the side "adjacent to angle B" and "opposed to" (or "opposite") "angle A", while side "b" is the side "adjacent to
Integer triangle "c" , "a" + "b" ≤ "c" and "a" ≤ "b" ≤ "c". This is also the number of integer sided obtuse or right (non-acute) triangles with largest side "c". The sequence starting at "c" = 1, is: Consequently, the difference between the two above sequences gives the number of acute integer sided triangles (up to congruence) with given largest side "c". The sequence starting at "c" = 1, is: By Heron's formula, if "T" is the area of a triangle whose sides have lengths "a", "b", and "c" then Since all the terms under the radical on the right