Question

4) As shown in the diagram below, a ship is heading directly toward a lighthouse whose beacon is 125 feet above sea level. At the first sighting, point A, the angle of elevation from the ship to the light was 7°, A short time later, at point D, the angle of elevation was 16 degrees.

To the nearest foot, determine and state how far the ship traveled from point A to point D.​

Answer 1

Check the picture below.

`\tan(16^o )=\cfrac{\stackrel{opposite}{125}}{\underset{adjacent}{y}} \implies y\tan(16^o)=125\implies y=\cfrac{125}{\tan(16^o)} \\\\[-0.35em] ~\dotfill\\\\ \tan(7^o )=\cfrac{\stackrel{opposite}{125}}{\underset{adjacent}{x+y}} \implies (x+y)\tan(7^o)=125\implies x+y=\cfrac{125}{\tan(7^o)} \\\\\\ x=\cfrac{125}{\tan(7^o)}-y\implies x=\cfrac{125}{\tan(7^o)}-\cfrac{125}{\tan(16^o)}\implies \boxed{x\approx 582~ft}`

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