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

1. Problem Description

We are asked to find the length of an arc intercepted by a central angle $\theta$ in a circle of radius $r$. We are given $r = 49.97$ ft and $\theta = \frac{\pi}{5}$ radians. We need to round the 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.

Given $r = 49.97$ ft and $\theta = \frac{\pi}{5}$ radians, we can substitute these values into the formula:

$s = 49.97 \cdot \frac{\pi}{5}$

Using the value $\pi \approx 3.14159$, we get:

$s = 49.97 \cdot \frac{3.14159}{5} \approx 49.97 \cdot 0.628318 \approx 31.39995$

Rounding to 1 decimal place, we get $s \approx 31.4$ ft.

3. Final Answer

31.4 ft