Height of an Equilateral Triangle
How to find the height of an equilateral triangle: definition, formula, proof, examples, and their solutions.
An equilateral triangle is a triangle
whose sides are all congruent.
(See its name: 'equi' + 'lateral'.)
Its interior angles are also all congruent: 60º.
If the equilateral triangle's side is a,
then the height of the equilateral triangle is
See the left half of the equilateral triangle (blue).
The measures of its interior angles are 60 and 90.
So this is a 30-60-90 triangle.
Draw a 30-60-90 triangle
next to the equilateral triangle.
(with its sides → 1 : √3: 2)
The right triangles are similar.
So set a proportion
between the right triangles' corresponding sides:
h / √3 = a / 2.
Similarity of sides in triangles
The equilateral triangle's side: 8
Height: h = (√3/2)⋅8
The equilateral triangle's side: x
Height: 12 = (√3/2)⋅x