Question

The measure of an angle in radians is the ratio of the arc length created by the angle to the circle’s radius. If the radius is 6 feet and the arc length is 2π
, then define the angle measure in radians.(1 point)
Responses

π3
Start Fraction pi over 3 End Fraction

6π
6 pi

12π
12 pi

3π
3 pi

Answer 1

The measure of an angle in radians is calculated using the formula:

\[
\theta = \frac{s}{r}
\]

where \(s\) is the arc length and \(r\) is the radius of the circle.

In this case, the radius \(r\) is 6 feet, and the arc length \(s\) is \(2\pi\) feet. Plugging the values into the formula:

\[
\theta = \frac{2\pi}{6}
\]

This simplifies to:

\[
\theta = \frac{\pi}{3}
\]

So the angle measure in radians is \(\frac{\pi}{3}\).

The correct response is:

\(\frac{\pi}{3}\)