An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are B = 8°and 8 = 12.5 (see figure). How far apart are the ships? (Round your answer to one decimal place.)

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AdrieneM94100 AdrieneM94100 · Answer 1 · 2022-11-03T11:52:15+01:00

ANSWER:

911.6 ft

EXPLANATION:

Given:

[tex]\begin{gathered} \theta=12.5^{\circ} \\ \beta=8^{\circ} \end{gathered}[/tex]

To find:

The distance between the two ships

Let's go ahead and draw a sketch as seen below;

Let's go ahead and solve for the value of AC by taking the tangent of angle 12.5 degrees as seen below;

[tex]\begin{gathered} \tan12.5=\frac{350}{AC} \\ \\ AC=\frac{350}{\tan12.5} \\ \\ AC=1578.7\text{ }ft \end{gathered}[/tex]

Let's now solve for the value of AD by taking the tangent of angle 8 degrees as seen below;

[tex]\begin{gathered} \tan8=\frac{350}{AD} \\ \\ AD=\frac{350}{\tan8} \\ \\ AD=2490.4\text{ }ft \end{gathered}[/tex]

Therefore the distance between the two ships will be;

[tex]\begin{gathered} CD=AD-AC \\ CD=2490.4-1578.7 \\ CD=911.6\text{ }ft \end{gathered}[/tex]

So the two ships are 911.6 ft