Question

Fort Forte is due north of camp Campbell. A Stealth helicaptor flight takes off from the fort and heads towards the camp. At one Point in the helicaptor flight it's in line of sight distance is 10 miles from the Fort at a angle of elevation of 27°. The chopper radios the camp and reports that they can see the camp at an angle of depression of 18°. How far apart are the two military installations?

Answer 1

the dark point is the helicaptor. So we get that the height of the helicaptor is

$\begin{gathered} 10\cdot\sin 27=h \\ h\approx4.54mi \end{gathered}$

So we get that

$\begin{gathered} x=10\cdot\cos 27\approx8.91mi \\ \tan (18)=\frac{4.54}{y}\rightarrow y=\frac{4.54}{\tan 18}\approx13.97mi \end{gathered}$

so the distance between the two military installations is

$x+y=8.91+13.97\approx22.88mi$