If a ferris wheel with a 20.5 meter radius, how high would one car be from the loding dock at these given angles trveled by the rider?:

90
135
180
225
270
315
405
450
495
and 540?

I will do of these,

for 135° :
assume the axle is 20.5 above the ground

height above axle:
sin135 = h/20.5
h = 20.5sin135 = appr 14.5 m
so height above the ground = 20.5 + 14.5 = 35

for 315°

height from axle :
sin 315 = h/20.5
h = 20.5sin135 = appr - 14.5
notice the position would be BELOW the axle
so height above ground = 20.5 - 14.5 = 6 m

To determine the height of the car, we need to find the vertical distance from the center of the ferris wheel to the car at each given angle. We can use trigonometry to do this.

The height of the car can be calculated using the formula:
h = r * sin(θ)

where:
h is the height of the car,
r is the radius of the ferris wheel, and
θ is the angle traveled by the rider.

Given that the radius of the ferris wheel is 20.5 meters, we can substitute this value into the formula to find the height of the car at each angle.

Let's calculate the height for each given angle:

1. At 90 degrees:
h = 20.5 * sin(90)
h = 20.5 * 1
h = 20.5 meters

2. At 135 degrees:
h = 20.5 * sin(135)
h ≈ 20.5 * 0.707
h ≈ 14.498 meters

3. At 180 degrees:
h = 20.5 * sin(180)
h = 20.5 * 0
h = 0 meters

4. At 225 degrees:
h = 20.5 * sin(225)
h ≈ 20.5 * -0.707
h ≈ -14.498 meters (negative because it is below the loading dock)

5. At 270 degrees:
h = 20.5 * sin(270)
h = 20.5 * -1
h = -20.5 meters (negative because it is below the loading dock)

6. At 315 degrees:
h = 20.5 * sin(315)
h ≈ 20.5 * -0.707
h ≈ -14.498 meters (negative because it is below the loading dock)

7. At 405 degrees:
h = 20.5 * sin(405)
h ≈ 20.5 * -0.707
h ≈ -14.498 meters (negative because it is below the loading dock)

8. At 450 degrees:
h = 20.5 * sin(450)
h = 20.5 * 0
h = 0 meters

9. At 495 degrees:
h = 20.5 * sin(495)
h ≈ 20.5 * 0.707
h ≈ 14.498 meters

10. At 540 degrees:
h = 20.5 * sin(540)
h = 20.5 * 1
h = 20.5 meters

Therefore, at the given angles:
90 degrees: 20.5 meters above the loading dock
135 degrees: 14.498 meters above the loading dock
180 degrees: at the same level as the loading dock
225 degrees: 14.498 meters below the loading dock
270 degrees: 20.5 meters below the loading dock
315 degrees: 14.498 meters below the loading dock
405 degrees: 14.498 meters below the loading dock
450 degrees: at the same level as the loading dock
495 degrees: 14.498 meters above the loading dock
540 degrees: 20.5 meters above the loading dock