To find the length of the arc of a circle given the radius and the central angle, you can use the formula:
\[ L = r \theta \]
where:
- \( L \) is the length of the arc,
- \( r \) is the radius of the circle, and
- \( \theta \) is the central angle in radians.
First, we need to convert the central angle from degrees to radians. The conversion formula is:
\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \]
For an angle of 105 degrees:
\[ \theta = 105 \times \frac{\pi}{180} = \frac{105\pi}{180} = \frac{7\pi}{12} \]
Now that we have the angle in radians, we can substitute the radius and the angle into the arc length formula:
\[ L = 7 \times \frac{7\pi}{12} \]
Calculating this gives:
\[ L = \frac{49\pi}{12} \]
Thus, the length of the arc is:
\[ \frac{49\pi}{12} \text{ yards} \]
This is the answer in terms of \(\pi\).