SOLUTION: Michael is sitting on a Ferris wheel. He is exactly 30 feet from the center and is at the 3 o'clock position when the Ferris wheel begins moving. The bottom of the Ferris wheel is
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Question 1101621: Michael is sitting on a Ferris wheel. He is exactly 30 feet from the center and is at the 3 o'clock position when the Ferris wheel begins moving. The bottom of the Ferris wheel is 6 feet above the ground. The Ferris wheel broke down within the first revolution of the ride when Michael was at the point (-9.22, -28.548).
a. What is the measure of the angle (in radians) that has a vertex (0,0)
and rays through the point (30,0) and (-9.22, -28.548)? Theta= Radians
b. How many feet did Michael travel along the arc before stopping? Feet Answer by greenestamps(13203) (Show Source):
The point (-9.22, -28.548) is indeed a point on the circle with center (0,0) and radius 30; so the given information is valid.
The reference angle for that point on the circle, measured to the "negative y axis" -- i.e., to the 9 o'clock position -- has a sine of 28.548/30 and a cosine of 9.22/30.
Using either inverse function shows the reference angle is 1.2584 radians.
The angle through which Michael travels in radians is .
That is the answer to part (a): 1.8832 radians.
The arc length that Michael traveled is simply the radian measure multiplied by the radius, which is 30: feet.
