Question

How to find the height of an equilateral triangle with side lengths of 20?

Answer 1

To find the height of an equilateral triangle, draw a line from the middle of the base to the vertex (meeting point) at the top of the triangle.
An equilateral triangle is also equiangular - meaning that its angles are all 60°.
By drawing a line down the middle of the triangle (see image), we effectively create a 30-60-90 triangle on both sides - the line splits the 60° angle at the top into 30 and 30, and the height line is perpendicular to the base, making a right angle.
The sides of a 30-60-90 triangle are x, 2x, and x√3, with x being the shortest side and 2x being the hypotenuse.
We already know what 2x is - it's the side length of the triangle, or 20.
If 20 = 2x, then we can easily figure out what the length of the short side, or half the base, is.
That leaves the medium-length side - the height side drawn down the middle of the triangle. Given that 20 = 2x and the last side is x√3, what is the height?

Hope this helps!
-refrac532