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

π3
Start Fraction pi over 3 End Fraction

6π
6 pi

3π
3 pi

12π

Answer 1

To find the angle measure in radians, we 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:

• \( s = 2\pi \) feet,
• \( r = 6 \) feet.

Substituting the values into the formula:

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

Thus, the angle measure in radians is

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

So the correct response is:

Start Fraction pi over 3 End Fraction