The altitude of an equilateral triangle is 18 inches. Find the length of a side

Let the length of equilateral triangle be x.

Each of the angle in an equilateral triangle is = 60°

The opposite to the 60° is the 18 inches. Hypotenuse is the side.

Sin 60° = 18 / Hypotenuse

Hypotenuse = 18 / Sin60°. Sin60° = √3 / 2

x = 18 / (√3 / 2)

= 18 / √3 * 2/1 = 36 / √3

x = 36 / √3

Rationalize the surd = 36 / √3 * (√3 / √3) = 36√3 / 3

x = 12√3 ≈ 12 * 1.732 ≈ 20.784

Length of side, x = 12√3 ≈ 20.784 inches.