Answer
The height of the wall is $\text{15}\text{.6 feet}$.
Work Step by Step
By observing the figure, we will find A.
We will use the linear pair of angles to get,
$\begin{align}
& A=90{}^\circ -6{}^\circ \\
& =84{}^\circ
\end{align}$
Now, to find angle C we will use the angle sum property of triangles:
$\begin{align}
& A+B+C=180{}^\circ \\
& 84{}^\circ +22{}^\circ +C=180{}^\circ \\
& C=180{}^\circ -106{}^\circ \\
& C=74{}^\circ
\end{align}$
Using the law of sines we will find a:
$\begin{align}
& \frac{a}{\sin A}=\frac{c}{\sin C} \\
& \frac{a}{\sin 22{}^\circ }=\frac{40}{\sin 74{}^\circ } \\
& c=\frac{40\sin 22{}^\circ }{\sin 74{}^\circ } \\
& \approx 15.6
\end{align}$
Therefore, the height of the wall is $\text{15}\text{.6 feet}$.
