Question

Elmer is on a ferris wheel which has a diameter of 170 ft and whose center is 105 ft off the ground. Find all of the angles θ such that 0≤θ≤3π and such that Elmer's carriage is at a height of 147.5 ft when it makes an angle of θ with the horizontal. Leave your answers in exact form.

Answer 1

To find the angles θ where Elmer's height is 147.5 ft on the Ferris wheel with a 170 ft diameter and center at 105 ft, we use the equation 147.5 = 105 + 85 * cos(θ) and solve for θ within the range 0 to 3π.

Step-by-step explanation:

The student is asking to find all the angles θ such that 0≤θ≤3π for a situation where a person named Elmer is on a Ferris wheel. Given that the Ferris wheel has a diameter of 170 ft and its center is 105 ft off the ground, we need to find the angles at which Elmer's carriage reaches a height of 147.5 ft.

First, to solve this, we calculate the radius of the Ferris wheel, which is half of the diameter, so R = 85 ft. The height above the ground at any point on the Ferris wheel is given by 105 ft + 85 ft * cos(θ). Therefore, to find the angles θ that give a height of 147.5 ft, we set up the equation:

147.5 = 105 + 85 * cos(θ)

Then we solve for θ within the given range 0 to 3π.