Question 203547
The altitude bisects the equilateral triangle into two congruent right triangles in which the altitude (of the equilateral triangle) is also the altitude (h) of both right triangles.
Using the Pythagorean theorem, we can find h in terms of the side (s) of the equilateral triangle.
{{{h^2 = s^2-(s/2)^2}}} Simplifying.
{{{h^2 = s^2-s^2/4}}}
{{{h^2 = (3/4)s^2}}} Taking the square root of both sides, we get:
{{{highlight(h = (sqrt(3)s)/2)}}}