Question

question 6 of 10
what is the length of the altitude of the equilateral triangle below?
a. ( 4sqrt{3} )
b. ( 8sqrt{3} )
c. 4
d. 1
e. 32
f. 8

Explanation:

Step1: Identify the triangle type

The triangle is a 30-60-90 right triangle (one angle 30°, one 60°, one 90°) with hypotenuse 8 and one leg (adjacent to 30°) 4.

Step2: Use Pythagorean theorem or 30-60-90 ratios

In a 30-60-90 triangle, the sides are in the ratio \(1 : \sqrt{3} : 2\) (shorter leg : longer leg : hypotenuse). Here, shorter leg is 4, so longer leg (altitude \(a\)) is \(4\sqrt{3}\) (since longer leg = shorter leg \(\times\sqrt{3}\)). Alternatively, using Pythagoras: \(a = \sqrt{8^2 - 4^2} = \sqrt{64 - 16} = \sqrt{48} = 4\sqrt{3}\).

Answer:

A. \(4\sqrt{3}\)