Question

The measure of an angle in radians is the ratio of the arc length crated 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.

a. π/3
b. 6π
c. 3π
d. 12π

Answer 1

To find the angle measure in radians using 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.

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

We can plug these values into the formula:

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

Now, simplify the fraction:

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

Thus, the angle measure in radians is:

\(\boxed{\frac{\pi}{3}}\) which corresponds to option a.