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.

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