What is the significance of the orthocenter of a triangle?

The point of intersection of the three altitudes of a triangle is called the orthocenter, and the altitudes can be used to calculate the area of a triangle. The altitudes can also be used to calculate the values of trigonometric ratios.

The altitude of a triangle is a line segment drawn from the vertex of a triangle and perpendicular to the opposite side of the triangle. In a right-angled triangle, the vertex forming the right angle is the orthocenter of the triangle. If the triangle has one angle greater than 90 degrees, the orthocenter lies outside the triangle. If all three angles of a triangle are less than 90 degrees, the orthocenter lies inside the triangle.