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

3π
3 pi

12π
12 pi

6π
6 pi
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Answer 1

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

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

where:
- \( \theta \) is the angle in radians,
- \( s \) is the arc length,
- \( r \) is the radius of the circle.

Given:
- Arc length \( s = 2\pi \) feet,
- Radius \( r = 6 \) feet.

Now, substitute the values into the formula:

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

Simplifying this gives:

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

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

The correct response is:

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