Question 376207
If you add an altitude to an equilateral triangle, you have a right triangle with hypotenuse {{{s}}}, leg {{{s/2}}}, and leg of altitude {{{h}}}.
Use the Pythagorean theorem,
{{{h^2+(s/2)^2=s^2}}}
{{{h^2+s^2/4=s^2}}}
{{{h^2=(3/4)s^2}}}
{{{h=(sqrt(3)/2)s}}}
So then the ratio of the altitude h to side s is
{{{highlight(h/s=sqrt(3)/2)}}}