Question
A Ferris wheel has a radius of 80 feet. Two particular cars are located such that the central angle between them is 165°. To the nearest tenth, what is the length of the intercepted arc between those two cars on the Ferris wheel?
Answers
GPT 3.5
To find the length of the intercepted arc, we first need to calculate the circumference of the Ferris wheel:
Circumference = 2 * π * radius
Circumference = 2 * π * 80
Circumference ≈ 502.7 feet
Next, we need to find the fraction of the circumference that the central angle of 165° represents:
Fraction of circumference = 165° / 360°
Fraction of circumference = 0.4583
Finally, we calculate the length of the intercepted arc:
Length of intercepted arc = Fraction of circumference * Circumference
Length of intercepted arc = 0.4583 * 502.7
Length of intercepted arc ≈ 230.1 feet
Therefore, the length of the intercepted arc between the two cars on the Ferris wheel is approximately 230.1 feet.
Circumference = 2 * π * radius
Circumference = 2 * π * 80
Circumference ≈ 502.7 feet
Next, we need to find the fraction of the circumference that the central angle of 165° represents:
Fraction of circumference = 165° / 360°
Fraction of circumference = 0.4583
Finally, we calculate the length of the intercepted arc:
Length of intercepted arc = Fraction of circumference * Circumference
Length of intercepted arc = 0.4583 * 502.7
Length of intercepted arc ≈ 230.1 feet
Therefore, the length of the intercepted arc between the two cars on the Ferris wheel is approximately 230.1 feet.