We are given a rectangular prism with a volume of $171.6$ cubic feet. The length of the prism is $11$ feet and the width is $2$ feet. We need to find the height of the prism to the nearest tenth of a foot.

1. Problem Description

We are given a rectangular prism with a volume of $171.6$ cubic feet. The length of the prism is $11$ feet and the width is $2$ feet. We need to find the height of the prism to the nearest tenth of a foot.

2. Solution Steps

The volume $V$ of a rectangular prism is given by the formula:

$V = l \times w \times h$

where $l$ is the length, $w$ is the width, and $h$ is the height. We are given that $V = 171.6$ cubic feet, $l = 11$ feet, and $w = 2$ feet. We need to find $h$.

$171.6 = 11 \times 2 \times h$

$171.6 = 22h$

$h = \frac{171.6}{22}$

$h = 7.8$

3. Final Answer

The height of the prism is $7.8$ feet.