Sketch an equilateral triangle with side lengths of 8 cm.

Question

Use special right triangle shortcuts to find the exact length of an altitude of the triangle.

Answer 1

Referring to this image, we can see that we can form 2 right triangles within the equilateral triangle by drawing a red line as shown.

Next, we can use the Pythagorean Theorem to solve for x (the height/altitude of the triangle)

Note that the base of one of the right triangles is 4 since it is equal to exactly half of the base length 8.

4² + x² = 8²

16 + x² = 64

x² = 48

x = √48

x = √16 · √3

x = 4√3

So the height/altitude of the triangle is 4√3