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 angle of rotation is 214°.

Explanation:

Formula for arc length:

The length of arc is the product of radius and the central angle ( in radian).

L= rθ

L= Length of arc

r= Radius

θ= Central angle (in radian).

Here L= 280 feet and diameter =150 feet.

Radius
`=(150)/(2)` feet =75 feet

L= rθ

`\Rightarrow \theta =(L)/(r)`

`\Rightarrow \theta =(280)/(75)` radian.

We know that,

π radian= 180°

`\Rightarrow 1 \ radian= (180^\circ)/(\pi)`

`\Rightarrow (280)/(75) \ radian = (180^\circ)/(\pi)* (280)/(75)`

= 214°

The angle of rotation is 214°.