Question

If the length of an arc of a circle is 44 inches, and the radius is 12 inches, what is the degree measure of the central angle to the nearest tenth of a degree?

(1 point)
Responses

420.2°420.2 degrees

308.4°308.4 degrees

210.1°210.1 degrees

4.6°

Answer 1

To find the degree measure of the central angle corresponding to an arc length, you can use the formula for the arc length \( L \):

\[
L = r \theta
\]

where:
- \( L \) is the arc length,
- \( r \) is the radius,
- \( \theta \) is the central angle in radians.

Given that the arc length \( L = 44 \) inches and the radius \( r = 12 \) inches, we can rearrange the formula to solve for \( \theta \):

\[
\theta = \frac{L}{r} = \frac{44}{12} \approx 3.6667 \text{ radians}
\]

Now, to convert radians to degrees, we use the conversion factor \( \frac{180}{\pi} \):

\[
\text{Degrees} = \theta \times \frac{180}{\pi}
\]

Substituting in our value for \( \theta \):

\[
\text{Degrees} \approx 3.6667 \times \frac{180}{\pi} \approx 3.6667 \times 57.2958 \approx 210.1
\]

Thus, the degree measure of the central angle to the nearest tenth of a degree is:

\[
\boxed{210.1^\circ}
\]

So, the correct choice is **210.1°**.