Answer
$20,417$ feet
Work Step by Step
Given \begin{equation}
d=\sqrt{1.5 h}.
\end{equation} We are given that $d = 175$ miles and want to find the altitude, $h$, of the plane. Set $d(h)= 175$. \begin{equation}
\begin{aligned}
175& = \sqrt{1.5 \cdot 24} \\
\left( 175 \right)^2&= \left( \sqrt{1.5 h} \right)^2\\
30625& = 1.5h\\
\frac{30625}{1.5}& = h\\
20,417&= h.
\end{aligned}
\end{equation} The height of the plane above the ground is about $20,417$ feet.
