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A boat is heading towards a lighthouse, where Brianna is watching from a vertical
distance of 124 feet above the water. Brianna measures an angle of depression to the
boat at point A to be 14°. At some later time, Brianna takes another measurement
and finds the angle of depression to the boat (now at point B) to be 57°. Find the
distance from point A to point B. Round your answer to the nearest tenth of a foot if
necessary.

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Check the picture below.  Make sure your calculator is in Degree mode.

[tex]tan(14^o )=\cfrac{\stackrel{opposite}{124}}{\underset{adjacent}{x}}\implies x=\cfrac{124}{tan(14^o)} \\\\\\ tan(57^o )=\cfrac{\stackrel{opposite}{124}}{\underset{adjacent}{y}}\implies y=\cfrac{124}{tan(57^o)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{distance from A to B}}{x-y\implies }\cfrac{124}{tan(14^o)}~~ - ~~\cfrac{124}{tan(57^o)} ~~ \approx ~~ 416.8~ft[/tex]

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