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

π3
Start Fraction pi over 3 End Fraction

3π
3 pi

6π

Answer 1

The measure of an angle in radians is given by the formula:

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

where \( \theta \) is the angle in radians, \( s \) 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.

Substituting these values into the formula:

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

Therefore, the angle measure in radians is:

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

So the correct response is:

Start Fraction pi over 3 End Fraction.