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)

Question

Responses

12π
12 pi

3π
3 pi

π3
Start Fraction pi over 3 End Fraction

6π

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.

Here, the arc length \( s = 2\pi \) and the radius \( r = 6 \) feet.

Substituting into the formula:

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

So the angle measure in radians is:

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

The correct response is:

π/3 or Start Fraction pi over 3 End Fraction.