Each side of an equilateral triangle measures 30cm. How do you determine the altitude of the triangle?

Mar 14, 2016

Since it is equilateral, we can cut it in half, into two triangles that are equal in area. They are both right triangles, which is what's important

Explanation:

We find, if we cut the base, the base of the two new triangles is $\frac{30}{2}$ cm, or 15 cm.

We know that the other two sides measure 30 cm. So, by Pythagorean theorem we can find the altitude.

The hypotenuse is 30, and one of the legs is 15. The altitude is just another leg. Note that the hypotenuse is always opposite the right angle.

Assuming the altitude is b.

${15}^{2} + {b}^{2} = {30}^{2}$

${b}^{2} = {30}^{2} - {15}^{2}$

${b}^{2} = 900 - 225$

${b}^{2} = 675$

$b = 15 \sqrt{3} \mathmr{and} 25.98$

Your altitude measures approximately $25.98$ cm.

Practice exercises:

1. ABC is an isosceles triangle. AB = AC. If BC measures 24 meters, and the height of the triangle, from midpoint of BC to point A measures 5 meters, find AB and AC.

Good luck!