Triangle FGH is an equilateral triangle with sides measuring 34 to the square root of 3 units. What is the height of the triangle?

We have an equilateral triangle which means all sides are of equal length. In this problem, sides are 34√3.

We bisect the equilateral triangle, then we have:

hypotenuse = 34√3

Base = (34√3) / 2 = 17√3

Solving for height, we use Pythagorean theorem:

(34√3) ² = (17√3) ² + h²

h = √2601

h = 51

The answer for the height is 51.