How do you use the Pythagorean Theorem to find the height of an equilateral triangle with side lengths?

Answer 1

You divide the equilateral into two right triangles and solve for the height. In other words, since the sides are equal divide on side in half. This give 1 side of X ( the original length ) and 1 side of 1/2 X. Now solve for the third side.
Edit: shouldn't but I will write it out for you.
The hypoteneuse X squared - ( 1/2 X squared ) = H squared.

Answer 2

Pythagorean Theorem Equilateral Triangle

Answer 3

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RE:
How do you use the Pythagorean Theorem to find the height of an equilateral triangle with side lengths?

Answer 4

since the triangle is equilateral, this means that all side lengths and angles are equal. Knowing this, you can go from the top point of the triangle, (or any point, i suppose), and divide the triangle in half, creating 2 right angles on the bottom. Now you have two right triangles, facing in opposite directions...
use the pythagorean theorem, only switched around. Since you are not looking for the hypotenuse, just the height, your new equation will be something like this (the a's and b's could be switched on your diagram):
a^2 = c^2 - b^2
just square root both sides and you have your height...^_^
hope this helps ^_^

Answer 5

ummm pythagorean theorem only works with rite triangles, so u'd need to divide the triangle in half. then youd subsitute the side lengths into a^2+b^=c^2....careful...u hav 2 divide the base length in 2!!!
(it looks something like this 2^2+x^2=7^2)
hope it helped

Answer 6

The pyth. theorem works with RIGHT triangles.