Question

How do you calculate the height of an equilateral triangle?

Answer 1

The height of the equilateral triangle is `h=(asqrt(3))/2`

Explanation:

If you draw a height in an equilateral triangle you can see that the triangle is divided in 2 right angled triangles in which: sides `a` are hypothenuses, height is one cathetus (common for both triangles), the other is equal to `a/2`, so if we use the Pythagorean theorem we get:

`(a/2)^2+h^2=a^2`

`h^2=a^2-(a/2)^2`

`h^2=a^2-a^2/4`

`h^2=3/4a^2`

`h=(asqrt(3))/2`