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

Answer:

The angle of rotation is 214°.

Step-by-step 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 $=\frac{150}{2}$ feet =75 feet

L= rθ

$\Rightarrow \theta =\frac{L}{r}$

$\Rightarrow \theta =\frac{280}{75}$ radian.

We know that,

π  radian= 180°

$\Rightarrow 1 \ radian= \frac{180^\circ}{\pi}$

$\Rightarrow \frac{280}{75} \ radian = \frac{180^\circ}{\pi}\times \frac{280}{75}$

                      = 214°

The angle of rotation is 214°.