An equilateral triangle has a side length of 6. What is the height of the triangle?

Answer 1

Start by drawing the triangle. Then draw the height. It'll make a right angle with the base and connect up to the vertex. You've now made a 30-60-90 triange, and the hypotenuse is 6.

30-60-90 triangles have sides in the rations 1:sqrt(3):2 From here there's two popular methods:

1. If the hypotenuse is 6, then the smallest side is 3, and the height is 3sqrt(3)
2. Set up a proportion 6/2=x/sqrt(3)

Hope that helps!

Answer 2

If you draw a line for the height, this splits the equilateral triangle into 2 triangles that are 30-60-90 and the side across from the 30 degree angle is 3, half of 6. This special triangle follows the pattern of 1-2-√3 for the sides. So this one would be 3-6-3√3

The height is 3√3