To find the degree measure of the central angle given the length of an arc and the radius of the circle, you can use the formula for the length of an arc:
\[ L = r \cdot \theta \]
where:
- \( L \) is the length of the arc,
- \( r \) is the radius of the circle,
- \( \theta \) is the central angle in radians.
First, we need to rearrange the formula to solve for \( \theta \):
\[ \theta = \frac{L}{r} \]
Substituting the given values (\( L = 44 \) inches and \( r = 12 \) inches):
\[ \theta = \frac{44}{12} = \frac{11}{3} \text{ radians} \]
Now, to convert radians to degrees, use the conversion factor \( \frac{180}{\pi} \):
\[ \text{degrees} = \theta \cdot \frac{180}{\pi} \]
Substituting the value we found:
\[ \text{degrees} = \left(\frac{11}{3}\right) \cdot \frac{180}{\pi} \]
Calculating this step-by-step:
\[ \text{degrees} \approx \frac{11 \cdot 180}{3 \cdot 3.14159} \approx \frac{1980}{9.42477} \approx 210.1 , \text{degrees} \]
So, to the nearest tenth of a degree, the measure of the central angle is:
\[ \boxed{210.1 \text{ degrees}} \]