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).

Answer:

The height of the equilateral triangle is (a/2) √3,

where a = length of a side of the triangle.