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A Ferris wheel has a radius of 30 feet. Two particular cars are located such that the central angle between them is 140°. To the nearest tenth, what is the length of the intercepted arc between those two cars on the Ferris wheel?

Respuesta :

Answer:

230.4

feet

Explanation:

arc length  

=

circumference  

×

fraction of circle

×

×

×

×

=

2

π

r

×

165

360

×

×

×

×

=

2

×

π

×

80

×

165

360

×

×

×

×

=

230.4

feet to nearest tenth

Step-by-step explanation:

oladayoademosu

The length of the intercepted arc between those two cars on the Ferris wheel is 73.3 ft

Since the distance between the two cars is the length of an arc, we need to know what the length of an arc is.

What is the length of an arc?

The length of an arc is given by L = Ф/360 × 2πr where

  • Ф = angle of arc and
  • r = radius of circle

Given that for the ferris wheel

  • Ф = 140° and
  • r = 30 ft

Substituting the values of the variables into the equation, we have

L = Ф/360 × 2πr

L = 140°/360 × 2π × 30 ft

L = 14/36 × 60π ft

L = 14/3 × 5π ft

L = 70π/3 ft

L = 219.91 ft/3

L = 73.3 ft

So, length of the intercepted arc between those two cars on the Ferris wheel is 73.3 ft

Learn more about length of an arc here:

https://brainly.com/question/8402454

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