Triangle fgh is an equilateral triangle with sides measuring units.

what is the height of the triangle?

gr= units

Draw an equilateral triangle FGH so that FH is the horizontal base. Draw a vertical line GR from G to line FH to represent the height of the triangle.

Let a = length of a side of the equilateral triangle (all sides are equal).
Each angle is 60° because the three angles add up to 180°.

Let h = GR, the height of the triangle.
Because the triangle is equilateral, triangle FGR is a right triangle, with
m∠F = 60° ,
m∠R = 90°,
FG = a.

By definition,
sin(F) = h/a
That is,
h = a*sin(F) = a*sin(60) = a*(√3/2).

The height of the equilateral triangle is (a/2)√3,
where a = length of a side of the triangle.