What is the length of the altitude of an equilateral triangle with side a?
1 answer:
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.
You might be interested in