Question

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.)

Answer 1

911.6 ft

Step-by-step explanation:

Given:

`\begin{gathered} \theta=12.5^(\circ) \\ \beta=8^(\circ) \end{gathered}`

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;

`\begin{gathered} \tan12.5=(350)/(AC) \\ \\ AC=(350)/(\tan12.5) \\ \\ AC=1578.7\text{ }ft \end{gathered}`

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

`\begin{gathered} \tan8=(350)/(AD) \\ \\ AD=(350)/(\tan8) \\ \\ AD=2490.4\text{ }ft \end{gathered}`

Therefore the distance between the two ships will be;

`\begin{gathered} CD=AD-AC \\ CD=2490.4-1578.7 \\ CD=911.6\text{ }ft \end{gathered}`

So the two ships are 911.6 ft