Question

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

3π
3 pi

6π
6 pi

12π
12 pi

π3

Answer 1

To find the angle measure in radians, you can use the formula:

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

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

Given:
- \( s = 2\pi \) feet (arc length)
- \( r = 6 \) feet (radius)

Now plug in the values:

\[
\theta = \frac{2\pi}{6} = \frac{\pi}{3}
\]

Thus, the angle measure in radians is:

\(\pi/3\) (or \(\frac{\pi}{3}\)).

So the correct response is:

\(\frac{\pi}{3}\) (or simply \(\pi3\) as per your format).