Question

What is the length of the altitude of an equilateral triangle with side a?

Answer 1

Answer:

  (a√3)/2

Step-by-step explanation:

You can find the height (h) of a equilateral triangle any of several ways. A simple one is to use the Pythagorean theorem.

In the diagram below, h is one leg of the right triangle with a/2 as the other leg and a as the hypotenuse. The Pythagorean theorem gives the relationship as ...

  h² + (a/2)² = a²

  h² = a² - a²/4 . . . . . . . subtract (a/2)²

  h² = a²(1 -1/4) = a²(3/4)

  h = √(a²(3/4)) = (a/2)√3

The height is (√3)/2 times the side length.