Question

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 16°18'. When the boat stops, the angle of depression is 48°51'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

Answer 1

check the picture below.

bearing in mind that there are 60 minutes in 1 degree, then 16°18' will be 16.3° and likewise 48°51' will be 48.85° if we convert those to degrees only.

$\bf y=\cfrac{200}{tan(48.85^o)}~\hspace{10em}x=\cfrac{200}{tan(16.3^o)}-y \\\\\\ x=\cfrac{200}{tan(16.3^o)}-\cfrac{200}{tan(48.85^o)}\implies x\approx 683.95 - 174.78\implies x\approx 509.17$