<P> In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). This line containing the opposite side is called the extended base of the altitude . The intersection of the extended base and the altitude is called the foot of the altitude . The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex . The process of drawing the altitude from the vertex to the foot is known as dropping the altitude at that vertex . It is a special case of orthogonal projection . </P> <P> Altitudes can be used in the computation of the area of a triangle: one half of the product of an altitude's length and its base's length equals the triangle's area . Thus, the longest altitude is perpendicular to the shortest side of the triangle . The altitudes are also related to the sides of the triangle through the trigonometric functions . </P>

What is a altitude of a triangle in geometry