Answer
The person's height above the ground is 75.0 feet.
Work Step by Step
If the wheel rotates through an angle of $\frac{2\pi}{3}~rad$, a person starting at the bottom of the wheel would be an angle of $\frac{\pi}{6}~rad$ above a horizontal line through the center of the wheel.
We can find the height $y$ above the center of the wheel:
$\frac{y}{r} = sin(\frac{\pi}{6})$
$y = (r)~sin(\frac{\pi}{6})$
$y = (r)~(\frac{1}{2})$
$y = (50.0~ft)~(\frac{1}{2})$
$y = 25.0~ft$
The person is 25.0 feet above the center of the wheel. Since the center of the wheel is 50.0 feet above the ground, the person's height above the ground is 25.0 feet + 50.0 feet which is 75.0 feet.
