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Altitude of an Equilateral Triangle. The altitude or height of an equilateral triangle is the line segment from a vertex that is perpendicular to the opposite side. It is interesting to note that the altitude of an equilateral triangle bisects its base and the opposite angle.
Altitude of an Equilateral Triangle. 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.
Get the formulas for Area of Equilateral triangle, Perimeter and Semi-perimeter of Equilateral triangle, Altitude of Equilateral triangle with solved examples at BYJU'S.
How to Find the Altitude of an Equilateral Triangle? The altitude of a triangle is another name for the height of a triangle. Therefore, the altitude of an equilateral triangle can be calculated using the formula, h = ½(√3a), where 'h' is the height and 'a' represents the side length.
The height of an equilateral triangle can be determined using the Pythagoras theorem. It is also called altitude of an equilateral triangle. As we know, an equilateral triangle has all equal sides. Now, if we drop an altitude from the apex of the triangle to the base, it divides the triangle into two equal right triangles.
May 9, 2023 · To derive the formula of altitude of an equilateral triangle, two different methods can be used. They are given below: Using Trigonometric Function. In the given ABC, AB = BC = AC, and AE is the altitude that divides the base BC equally into BE and EC. In ABC, sin60° = Perpendicular/Hypotenuse. √3/2 = h/a [∵ sin60 = √3/2] h = √3/2a.
The altitude of a triangle formula for an equilateral triangle is expressed as: h= (a√ 3)/2. Where 'a' is the side of an equilateral triangle. What Is the Altitude of A Triangle Formula for a Right Triangle?
Jul 4, 2024 · The altitudes, the angle bisectors, the perpendicular bisectors, and the medians coincide. The equilateral triangle is a special case of an isosceles triangle, having not just two but all three sides equal. If you would like to learn more about the isosceles triangle, our isosceles triangle calculator is just the tool you need.
An altitude of an equilateral triangle is also an angle bisector, median, and perpendicular bisector. The three altitudes of an equilateral triangle intersect at a single point. The three altitudes extending from the vertices A, B, and C of ABC above intersect at point G.
Solution. Let ABC be an equilateral triangle of side 'a' units and AD be the altitude of the triangle. In ∆ABD, AB = a units. BD = a 2 units. Using pythagoras theorem, A B 2 = B D 2 + A D 2 ⇒ a 2 = a 2 2 + A D 2 ⇒ A D 2 = a 2 - a 2 4 ⇒ A D 2 = 4 a 2 - a 2 4 ⇒ A D 2 = 3 a 2 4 ⇒ A D = 3 2 a... 1. Now, Side Altitude = A B A D = a 3 2 a = 2 3.
