Question

Elmer is on a Ferris wheel which has a diameter of 180 and whose center is 120 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 165 when it makes an angle of θ with the horizontal. Leave your answers in exact form.

Answer 1

To find the angles θ when Elmer's carriage is at a certain height on the Ferris wheel, we can use trigonometry to set up an equation and solve for θ.

Step-by-step explanation:

To find all the angles θ such that Elmer's carriage is at a height of 165 when it makes an angle of θ with the horizontal on a Ferris wheel, we can use trigonometry. Given that the Ferris wheel has a diameter of 180 and a center that is 120 off the ground, we can find the radius by dividing the diameter by 2, which is 90. Now we can draw a right triangle with the radius as the hypotenuse, the height of the center as the adjacent side, and the height of the carriage as the opposite side. Using the sine function, we can set up the equation sin(θ) = 165/90 to find the value of θ. Solving for θ gives us:

θ = arcsin(165/90)