To find the apothem of a regular pentagon, we can use the formula that relates the radius (\( R \)) and the apothem (\( a \)):
\[ a = R \cdot \cos\left(\frac{\pi}{n}\right) \]
where \( n \) is the number of sides of the polygon. For a pentagon, \( n = 5 \).
Given:
- Radius \( R = 15 \) inches
- Number of sides \( n = 5 \)
Now, we calculate the angle:
\[ \frac{\pi}{n} = \frac{\pi}{5} \]
Next, we compute \( \cos\left(\frac{\pi}{5}\right) \):
\[ \cos\left(\frac{\pi}{5}\right) \approx 0.8090 \]
Now, we can find the apothem:
\[ a = 15 \cdot \cos\left(\frac{\pi}{5}\right) \approx 15 \cdot 0.8090 \approx 12.135 \]
Finally, rounding to two decimal places, we have:
\[ a \approx 12.14 \text{ inches} \]
Thus, the apothem of the pentagon is approximately 12.14 inches.