Question

a seat on a ferris wheel is level with the center of the wheel. the diameter of the wheel is 200 feet. suppose the wheel rotates 60°, causing the height of the seat to decrease. how much closer to the ground is the seat after the rotation? 50 feet 50√3 feet 100 feet 100√3 feet

Explanation:

Step1: Determine the radius

The diameter of the Ferris - wheel is $d = 200$ feet, so the radius $r=100$ feet.

Step2: Use trigonometry

We consider a right - triangle formed by the radius, the vertical line from the center of the Ferris - wheel to the seat's new position, and the line from the center of the Ferris - wheel to the seat's new position. The angle of rotation is $\theta = 60^{\circ}$. The vertical distance $y$ from the center of the Ferris - wheel to the seat's new position can be found using the sine function. $\sin\theta=\frac{y}{r}$.
Since $r = 100$ feet and $\theta = 60^{\circ}$, and $\sin60^{\circ}=\frac{\sqrt{3}}{2}$, we have $y = r\sin\theta=100\times\frac{\sqrt{3}}{2}=50\sqrt{3}$ feet.

Answer:

B. $50\sqrt{3}$ feet