Answer
The length of the pole is $\text{30}\text{.0 feet}$.
Work Step by Step
By observing the figure, we will find B.
Using the linear pair of angles we get,
$\begin{align}
& B=90{}^\circ -8{}^\circ \\
& =82{}^\circ
\end{align}$
Using the angle sum property of the triangle:
$\begin{align}
& A+B+C=180{}^\circ \\
& 62{}^\circ +82{}^\circ +C=180{}^\circ \\
& C=180{}^\circ -144{}^\circ \\
& C=36{}^\circ
\end{align}$
Using the law of sines we will find a:
$\begin{align}
& \frac{a}{\sin A}=\frac{c}{\sin C} \\
& \frac{a}{\sin 62{}^\circ }=\frac{20}{\sin 36{}^\circ } \\
& c=\frac{20\sin 62{}^\circ }{\sin 36{}^\circ } \\
& \approx 30.0
\end{align}$
Therefore, the length of the pole is $\text{30}\text{.0 feet}$.
