Question

The diameter of a Ferris wheel is 205 feet. The top of the wheel stands 217 feet above the ground. The figure below is a model of the Ferris wheel with angle θ the central angle that is formed as a rider moves from the initial position P0 to position P1. The rider is h feet above the ground at position P1. (Round your answers to the nearest whole number.)
(a) Find h if θ is 120.0°.
(b) Find h if θ is 210.0°.
(c) Find h if θ is 315.0°.

Answer 1

What is the radius of the circle?

Answer 2

Remember
Diameter = 2* radius

Answer 3

The radius is 102.5

Answer 4

Good.
Now notice the height of the uppermost point of the wheel.

Answer 5

What is x?

Answer 6

x is the height

Answer 7

@mathstudent55

Answer 8

x is the height above ground that the bottom of the wheel is at.
Can you calculate x from the picture I drew?

Answer 9

Remember that the diameter of the wheel is 205 ft, but the uppermost point of the wheel is at a height of 217 ft. That shows that the bottom of the wheel is not at ground level, but some feet above ground level. How many feet above ground level is the bottom of the wheel?

Answer 10

Would it be 12 ft?

Answer 11

Correct.
We need to keep the 12 ft distance in mind.

Answer 12

Now let's turn to the wheel itself.
The first angle is 120 deg which I drew above.

Answer 13

At what height is the center of the wheel?

Answer 14

114.5

Answer 15

Great.
Now we finally turn to the main part of the problem, which is dealing with the height based on the angle. We start with an angle of 120 degrees as shown in the figure.
We can break up that angle into tow adjacent angles, a 90-degree angle and a 30-degree angle.