Certainly! Let's calculate the radius of a circle given that we have a central angle of 45° and an arc length of 10.5 inches.
### Step-by-Step Solution:
1. Understand the relationships:
- The arc length (s) of a circle is given by the formula:
[tex]\[ s = r \theta \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle and [tex]\( \theta \)[/tex] is the central angle in radians.
2. Convert the central angle to radians:
- To convert degrees to radians, you use the conversion factor:
[tex]\[ \theta_{\text{radians}} = \theta_{\text{degrees}} \times \left(\frac{\pi}{180}\right) \][/tex]
- Given the central angle [tex]\( \theta = 45^\circ \)[/tex], we convert it to radians:
[tex]\[ \theta_{\text{radians}} = 45 \times \left(\frac{\pi}{180}\right) \approx 0.7854 \text{ radians} \][/tex]
3. Use the arc length formula:
- We are given the arc length [tex]\( s = 10.5 \)[/tex] inches. Now, using the formula [tex]\( s = r \theta \)[/tex]:
[tex]\[ r = \frac{s}{\theta} \][/tex]
- Substitute the given values into the formula:
[tex]\[ r = \frac{10.5}{0.7854} \][/tex]
4. Calculate the radius:
- Compute the radius from the formula above:
[tex]\[ r \approx \frac{10.5}{0.7854} \approx 13.38 \text{ inches} \][/tex]
So, the radius of the circle is approximately 13.38 inches.
Hence, the correct option is:
- approximately 13.38 inches
