A right triangle (American English) or right-angled triangle (British), or more formally an orthogonal triangle, formerly called a rectangled triangle (), is a triangle in which one angle is a right angle (that is, a 90-degree angle), i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry. The side opposite to 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 angle A and opposed to angle B. If the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple. Principal properties Area As with any triangle, the area is equal to one half the base multiplied by the corresponding height. In a right triangle, if one leg is taken as the base then the other is height, so the area of a right triangle is one half the product of the two legs. As a formula the area T is where a and b are the legs of the triangle. If the incircle is tangent to the hypotenuse AB at point P, then denoting the semi-perimeter as s, we have and , and the area is given by This formula only applies to right triangles. Altitudes If an altitude is drawn from the vertex with the right angle to the hypotenuse then the triangle is divided into two smaller triangles which are both similar to the original and therefore similar to each other. From this: The altitude to the hypotenuse is the geometric mean (mean proportional) of the two segments of the hypotenuse. Each leg of the triangle is the mean proportional of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg. In equations, (this is sometimes known as the right triangle altitude theorem) where a, b, c, d, e, f are as shown in the diagram. Thus Moreover, the altitude to the hypotenuse is related to the legs of the right triangle by For solutions of this equation in integer values of a, b, f,