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The altitude of a triangle is the perpendicular drawn from the vertex of the triangle to the opposite side. Also, known as the height of the triangle, the altitude makes a right-angle triangle with the base.
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- How to Find The Altitude of A Triangle?
- Altitude Formula
- Altitude of A Scalene Triangle
- Altitude of An Isosceles Triangle
- Altitude of An Equilateral Triangle
- Altitude of A Right Triangle
- Altitude of An Obtuse Triangle
Let us learn how to find out the altitude of a scalene triangle, equilateral triangle, right triangle, and isosceles triangle.
The important formulas for the altitude of a triangle are summed up in the following table. The following section explains these formulas in detail.
A scalene triangle is one in which all three sides are of different lengths. To find the altitude of a scalene triangle, we use the Heron's formula as shown here. h=2√s(s−a)(s−b)(s−c)bh=2s(s−a)(s−b)(s−c)bHere, h = height or altitude of the triangle, 's' is the semi-perimeter; 'a, 'b', and 'c' are the sides of the triangle. The steps to derive the f...
A triangle in which two sides are equal is called an isosceles triangle. The altitude of an isosceles triangle is perpendicularto its base. Let us see the derivation of the formula for the altitude of an isosceles triangle. In the isosceles triangle given above, side AB = AC, BC is the base, and AD is the altitude. Let us represent AB and AC as 'a'...
A triangle in which all three sides are equal is called an equilateral triangle. Considering the sides of the equilateral triangle to be 'a', its perimeter = 3a. Therefore, its semi-perimeter (s) = 3a/2 and the base of the triangle (b) = a. Let us see the derivation of the formula for the altitude of an equilateral triangle. Here, a = side-length o...
A triangle in which one of the angles is 90° is called a right triangle or a right-angled triangle. When we construct an altitude of a triangle from a vertex to the hypotenuse of a right-angled triangle, it forms two similar triangles. It is popularly known as the Right triangle altitude theorem. Let us see the derivation of the formula for the alt...
A triangle in which one of the interior angles is greater than 90° is called an obtuse triangle. The altitude of an obtuse triangle lies outside the triangle. It is usually drawn by extending the base of the obtuse triangle as shown in the figure given below. We know that the median and the altitude of a triangle are line segments that join the ver...
May 9, 2023 · Definition. Altitude or height of a triangle is the perpendicular line drawn from the vertex of a triangle to its opposite side. It makes a right angle with the base of the triangle. Altitude of a Triangle. Each triangle has three possible altitudes. Different triangles have different types of altitudes.
In geometry, an altitude of a triangle is a line segment through a given vertex (called apex) and perpendicular to a line containing the side or edge opposite the apex (the base ). This (infinite) line containing the (finite) base is called the extended base of the altitude.
The altitude of a triangle is a line from a vertex to the opposite side, that is perpendicular to that side, as shown in the animation above. A triangle therefore has three possible altitudes. The altitude is the shortest distance from a vertex to its opposite side.
An altitude is a perpendicular segment drawn from a vertex to the opposite side or extension of the opposite side. In other words, it's a line segment that drops down vertically from a vertex to the base of the triangle. The altitude also represents the triangle's height.
Jan 7, 2024 · The altitude of a triangle is a line segment that extends from a vertex (or corner) of the triangle to the base (or bottom line), forming a right angle (90 degrees) with the base. The altitude can be inside or outside the triangle depending on whether the triangle is acute or obtuse respectively.
