Question

A particular airport has beacons on the ground 6 km out from the start of each runway. Anairplane is directly over this beacon and is at an angle of elevation from the runway of 10°.Calculate the direct line distance from the airplane to the start of the runway

Answer 1

The situation described in the problem can be seen in the following diagram:

The direct line distance from the plane to the runway is the hypotenuse of the right triangle in the diagram. From the triangle we have:

$\begin{gathered} \cos 10=\frac{6}{d} \\ d=\frac{6}{\cos 10} \\ d=6.09 \end{gathered}$

Therefore the direct line distance is 6.09 km (rounded to two decimal places)