Step-by-step Solution:

The length of the pendulum corresponds to the radius (r) of the circular path it creates. The path it swings through is an arc of this circle.

1. Identify the given information and the relevant formula:
Length of the arc, \(L = 17.6\) cm.
Angle of the sector, \(\theta = 30^\circ\).
The formula connecting these variables is the formula for the length of a circular arc:
\[L = \frac{\theta}{360^\circ} \times 2\pi r\]
2. Rearrange the formula to solve for the length of the pendulum (r):
We need to isolate \(r\) in the formula to find the pendulum's length.
\[r = \frac{L \times 360^\circ}{2\pi\theta}\]
3. Substitute the given values and calculate:
Based on the numbers involved, we will use the common approximation \(\pi \approx \frac{22}{7}\).
\[\begin{aligned} r &= \frac{17.6 \times 360}{2 \times (\frac{22}{7}) \times 30} \\ &= \frac{17.6 \times 360 \times 7}{2 \times 22 \times 30} \\ &= \frac{17.6 \times 360 \times 7}{44 \times 30} \\ &= \frac{17.6 \times 12 \times 7}{44} \end{aligned}\]
To simplify the calculation, notice that \(17.6 \times 10 = 176\) and \(44 \times 4 = 176\), so \(\frac{17.6}{44} = 0.4\).
\[\begin{aligned} r &= 0.4 \times 12 \times 7 \\ &= 4.8 \times 7 \\ &= 33.6 \text{ cm} \end{aligned}\]
Result:
The length of the pendulum is 33.6 cm.