Question

A lighthouse that is 36 ft tall stands on the shore of lake michigan. Looking out from atop the lighthouse, a ship suddenly appears on the horizon. Approximately how far is the ship from the shore?

Answer 1

The distance (in miles) viewable to horizon of a lighthouse oh height h (in feet) is given by approximately

$\sqrt{ \frac{7h}{4} }$

Given that a lighthouse that is 36 ft tall stands on the shore of Lake Michigan, the distance of the boat it can see on the horizon is given by approximately

$\sqrt{ \frac{7\times36}{4} } = \sqrt{63} \approx7.94$