A car entered a roundabout from Mason Avenue, traveled 280 feet, then turned onto Perry Street. If the roundabout has a diameter

Question

3 months ago

6

of 150 feet, find the angle of rotation to the nearest degree the car traveled

1 answer:

Leona [12.6K] · Answer 1 · 2026-03-02T09:45:25+03:00

Answer:

The rotation angle measures 214°.

Step-by-step explanation:

Arc length formula:

The arc length equals the radius multiplied by the central angle (in radians).

L= rθ

L= Arc length

r= Radius

θ= Central angle (in radians).

Given L= 280 feet and diameter =150 feet.

Radius $=\frac{150}{2}$ feet =75 feet

L= rθ

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

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

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 rotation angle measures 214°.