The altitude of a triangle is defined as the line drawn from the vertex of a triangle and perpendicular to the opposite side of the triangle. A triangle has three sides and three vertices. Hence, it has three altitudes.
Altitudes may also lie outside a triangle. In a triangle with all three acute angles, all altitudes lie within the triangle. For an obtuse angled triangle, one or more altitudes may lie outside the triangle.
The altitudes of a triangle are useful when calculating the area of the triangle. The area of a triangle is half the product of its base and the corresponding altitude.
All three altitudes of a triangle intersect at a point called the orthocenter. The orthocenter may lie inside or outside the triangle.