The problem asks us to find the length of an arc intercepted by a central angle $\theta$ in a circle of radius $r$. We are given that $r = 49.97$ ft and $\theta = \frac{\pi}{5}$ radians. We need to round our answer to 1 decimal place.

1. Problem Description

The problem asks us to find the length of an arc intercepted by a central angle $\theta$ in a circle of radius $r$. We are given that $r = 49.97$ ft and $\theta = \frac{\pi}{5}$ radians. We need to round our answer to 1 decimal place.

2. Solution Steps

The formula for the arc length $s$ is given by:

$s = r\theta$

Where $r$ is the radius and $\theta$ is the central angle in radians.

In this case, $r = 49.97$ ft and $\theta = \frac{\pi}{5}$ radians.

So, $s = 49.97 \times \frac{\pi}{5}$.

Using $\pi \approx 3.14159$, we get $\frac{\pi}{5} \approx \frac{3.14159}{5} \approx 0.628318$.

$s = 49.97 \times 0.628318 \approx 31.396 \approx 31.4$ ft (rounded to 1 decimal place).

3. Final Answer

$31.4$ ft