Two boats

Two boats are located from a height of 150m above the lake's surface at depth angles of 57° and 39°. Find the distance of both boats if the sighting device and both ships are in a plane perpendicular to the lake's surface.

Final Answer:

x =  87.8234 m

Step-by-step explanation:

$$\begin{gathered} h=150\text{m} \\ \alpha =57{}^{\circ } \\ \beta =39{}^{\circ } \\ \tan \alpha =h:x_1 \\ \tan \beta =h:x_2 \\ {x}_1=h/\tan \alpha =h/\tan 57°=150/\tan 57°=150/1.539865=97.41114\text{m} \\ {x}_2=h/\tan \beta =h/\tan 39°=150/\tan 39°=150/0.809784=185.23457\text{m} \\ \alpha >\beta ,x_2>x_1 \\ x=|x_1-x_2|=|97.4111-185.2346|=87.8234\text{m} \end{gathered}$$

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