Step 1 :We are given the radius of the circle, \(r = 10.2\) cm, and the central angle, \(\theta = \frac{7\pi}{5}\) radians.
Step 2 :The length of an arc in a circle is given by the formula \(s = r\theta\), where \(s\) is the arc length, \(r\) is the radius of the circle, and \(\theta\) is the central angle in radians.
Step 3 :Substitute the given values into the formula to find the length of the arc: \(s = 10.2 \times \frac{7\pi}{5}\).
Step 4 :After calculating the arc length and rounding to one decimal place, we find that \(s \approx 44.9\) cm.
Step 5 :Final Answer: The length of the intercepted arc is approximately \(\boxed{44.9}\) cm.