Answer
$266.67$ feet
Work Step by Step
Given
\begin{equation}
d=\sqrt{1.5 h}.
\end{equation} We are given that $d=20$ miles and want to find how high, $h$, off the ground a person can see to the horizon. Set $d(h)=20$ and solve for $h$.
\begin{equation}
\begin{aligned}
20 & =\sqrt{1.5 h} \\
(20)^2 & =(\sqrt{1.5 h})^2 \\
400& =1.5 h \\
\frac{400}{1.5} & =h \\
h&\approx 266.67.
\end{aligned}
\end{equation} A person's eyes have to be about $266.67$ feet off the ground to see $20$ miles to the horizon.
