Question

A car entered a roundabout from Mason Avenue, traveled 280 feet,

then turned onto Perry Street. If the roundabout has a diameter of
150 feet, find the angle of rotation to the nearest degree the car
traveled.​

Answer 1

The nearest degree the car traveled is 146.2°

Explanation:

The diameter of the roundabout = 150ft

Radius (r) = 150/2

= 75ft

Circumference of the roundabout is given by,

C = 2πr

C = 2π (75)

C = 2(3.142) (75)

C = 471.3 ft

If the car travel 471.3 ft around the roundabout then it denotes that it traveled 360° . But the car traveled 280ft.

So,

The angle traveled by the car = (280/471.3) x 360°

= 0.594 x 360°

= 213.8°

The car traveled 213.8° .

The nearest degree= 360° - 213.8°

= 146.2°

The nearest degree the car traveled is 146.2°.