Altitude of a Triangle

An altitude of a given triangle is a line segment that passes through a vertex and is perpendicular to (i.e. forms a right angle with) the baseline (the side opposite the vertex). The expanded base of the altitude is the line that has the opposing side. The foot of the mentioned altitude is the point where the extended base coincides or meets the altitude. The distance between the extended base and the vertex is known as the length of the altitude, or simply “the altitude.” Dropping the altitude at that vertex is the process of making an altitude from the vertex to the foot. It’s a type of orthogonal projection that’s a little different.

The area of a given triangle can be calculated using altitudes: one half of the product of an altitude’s length and its base’s length equals the triangle’s area. Which results, in the largest altitude, is perpendicular to the given triangle’s shortest side. Through the trigonometric functions, the heights are also joined to the given triangle’s sides. The height with the incongruent side as its base will have the midpoint of that side as its foot in an isosceles triangle (a triangle with two congruent sides). The angle bisector of the vertex angle will also be the altitude with the incongruent side as its base.

The feet of the elevations all fall on the triangle’s sides in acute triangles (not extended). The foot of the height to the obtuse-angled vertex falls in the interior of the opposing side of an obtuse triangle (one with an obtuse angle), but the feet of the altitudes to the acute-angled vertices fall on the other extended side, exterior to the triangle. The following diagram shows how an altitude lowered perpendicularly from the top vertex, which has an acute angle, intersects the extended horizontal side outside the triangle in an obtuse triangle.

A perpendicular path traced from the vertex of a triangle to the opposite side is called the height of a triangle. Because a triangle has three sides, it may be divided into three altitudes. The elevations of different triangles are varied. The altitude of a triangle, also known as its height, is used to calculate its area and is represented by the letter ‘h’.

Definition of Triangle Altitude

An altitude is the perpendicular line segment traced from the triangle’s vertex to the opposite side. With the base of the given triangle it touches, the altitude forms a right angle. It is frequently referred to as a triangle’s height and is represented by the letter ‘h.’ The distance between the vertex and its opposing side can be calculated to determine its size. It’s worth noting that each of the triangle’s vertices can be used to draw three elevations. Look at the triangle below and find the spot where the triangle’s three altitudes meet. The ‘Orthocenter’ is the name given to this location.

Three elevations are possible in a triangle.

• Depending on the type of triangle, the elevations can be inside or outside the triangle.
• The altitude forms a 90° angle with the side opposite it.
• The orthocenter of a triangle is the place where the three elevations of the triangle intersect.

Definition of Triangle Altitude

An altitude is the perpendicular line segment traced from the triangle’s vertex to the opposite side. With the base of the given triangle it touches, the altitude forms a right angle. It is frequently referred to as a triangle’s height and is represented by the letter ‘h.’ The distance between the vertex and its opposing side can be calculated to determine its size. It’s worth noting that each of the triangle’s vertices can be used to draw three elevations. Look at the triangle below and find the spot where the triangle’s three altitudes meet. The ‘Orthocenter’ is the name given to this location.

• The altitude of a right triangle is:

A right triangle, also known as a right-angled triangle, is a triangle in which one of the angles is 90 degrees. When we build a triangle’s altitude from the vertex to the hypotenuse of a right-angled triangle, we get two comparable triangles.

• An obtuse triangle’s altitude is-

An obtuse triangle is defined as a triangle with one of its inner angles greater than 90 degrees. An obtuse triangle’s altitude is located on the outside of the triangle.

Points To Remember:

The following is a list of some key points about a triangle’s altitude.

• The orthocenter is the point where all three elevations of a triangle intersect.
• The orthocenter and the altitude might both be inside or outside the triangle.
• The altitude of a given equilateral triangle is the same as the triangle’s median.