Question 959628
The height cuts the equilateral triangle into two 30-60-90 special triangles.


x, the side of the equilateral triangle.
{{{x^2=(8.5)^2+(x/2)^2}}}----Pythagorean Theorem Relationship

{{{x^2=(1/4)x^2+8.5^2}}}
{{{(3/4)x^2=8.5^2}}}
{{{x^2=(8.5^2)/(3/4)}}}
{{{x^2=(4/3)(17/2)^2}}}
{{{x=(2*17)/(2*sqrt(3))}}}
{{{highlight(x=17/sqrt(3))}}}------rationalize if you want.