Answer
The length of the pier is $\text{81}\text{.0 feet}$.
Work Step by Step
We will find B by observing the given figure.
Using the linear pair of angles:
$\begin{align}
& B+85{}^\circ =180{}^\circ \\
& B=180{}^\circ -85{}^\circ \\
& B=95{}^\circ
\end{align}$
Now, we will find angle C.
Using the angle sum property of the triangle we get,
$\begin{align}
& A+B+C=180{}^\circ \\
& 37{}^\circ +95{}^\circ +C=180{}^\circ \\
& C=180{}^\circ -132{}^\circ \\
& C=48{}^\circ
\end{align}$
Using the law of sines we will find a:
$\begin{align}
& \frac{a}{\sin A}=\frac{c}{\sin C} \\
& \frac{a}{\sin 37{}^\circ }=\frac{100}{\sin 48{}^\circ } \\
& a=\frac{100\sin 37{}^\circ }{\sin 48{}^\circ } \\
& \approx 81.0
\end{align}$
Therefore, the length of the pier is $\text{81}\text{.0 feet}$.
