If a person on the Ferris wheel is 45 feet above the ground. The Gris wheel has a radius of 47.f and is 5 feet above the ground. At what degrees had the Ferris wheel rotated counted clockwise?
bottom of wheel up 5 so height above wheel bottom = 40
distance below center = 47 -40
cos A = 7/47
A = 81.4 degrees
To find the angle at which the Ferris wheel has rotated, we can use trigonometry.
First, let's draw a diagram to visualize the situation. The Ferris wheel can be represented by a circle, with its center at the origin (0,0). The radius of the Ferris wheel is 47 feet, and it is elevated 5 feet above the ground. The person on the Ferris wheel is 45 feet above the ground, so their height above the center of the Ferris wheel is 47 + 5 + 45 = 97 feet.
Now, let's consider a right triangle within the circle. One leg of the triangle is the vertical distance from the center of the Ferris wheel to the person (97 ft), and the other leg is the horizontal distance from the center of the Ferris wheel to the person, which is the radius of the Ferris wheel (47 ft).
Using the Pythagorean theorem, we can find the hypotenuse of this triangle, which represents the radial distance from the center of the Ferris wheel to the person:
hypotenuse^2 = vertical distance^2 + horizontal distance^2
hypotenuse^2 = 97^2 + 47^2
hypotenuse^2 = 9409 + 2209
hypotenuse^2 = 11618
hypotenuse ≈ √11618
hypotenuse ≈ 107.76 ft
Now, we can use inverse trigonometric functions to find the angle at which the Ferris wheel has rotated. We'll use the arctan function:
angle = arctan(opposite / adjacent)
angle = arctan(97 / 47)
angle ≈ 63.44 degrees
Therefore, the Ferris wheel has rotated approximately 63.44 degrees counterclockwise.