#### Answer

$9.9 \text{ miles}$

#### Work Step by Step

The variation model described by the problem is $
d=k\sqrt{e}
,$ where $d$ is the distance to the horizon and $e$ is the elevation of the observer.
Substituting the given values in the variation model above results to
\begin{array}{l}\require{cancel}
7.4=k\sqrt{36}
\\\\
7.4=k(6)
\\\\
\dfrac{7.4}{6}=k
.\end{array}
Therefore, the variation equation is $
d=\dfrac{7.4}{6}\sqrt{e}
.$
Using the variation equation above, then
\begin{array}{l}\require{cancel}
d=\dfrac{7.4}{6}\sqrt{64}
\\\\
d=\dfrac{7.4}{6}(8)
\\\\
d=9.8666666666666666666666666666667
.\end{array}
Rounded to the nearest tenth, the distance to the horizon is $
9.9 \text{ miles}
.$