The perimeter of an equilateral triangle is 32centimeters find the length of an altitude of the triagle to the nearest tenth of a centimeter?

Since an equilateral triangle has three congruent sides (and 3 congruent angles, each of 60⁰), the length of each side is 32/3 cm.

If we draw one of the altitudes of the triangle, then a right triangle is formed where the side of a triangle is the hypotenuse, and the altitude is opposite to a 60 degrees angle. So we have,

sin 60⁰ = altitude/(32/3 cm) (multiply by 32/3 cm to both sides)

(32/3 cm)sin 60⁰ = altitude

9.2 cm = altitude