A plane is flying at 300 meters altitude.  A man from the plane observes two man in a straight line on the same slides of the plane on the ground with angles of depression as 30° and 60°.  The distance between two men is?  (\(\sqrt {3}\) = 1.732)

346.4

C is man 1 and D is man 2.

CD is the distance between two men.

In ΔABD → Tan 30° = \(\frac{300}{BD}\)

BD = \(\frac{300}{\frac{1}{\sqrt {3}}}\)

In ΔABC → Tan 60° = \(\frac{300}{BC}\)

BC = \(\frac{300}{\sqrt {3}}\) = 100\(\sqrt {3}\)

Distance between two men on the ground

CD = BD - BC

= 300\(\sqrt {3}\) - 100\(\sqrt {3}\)

= 200\(\sqrt {3}\)

= 200 × 1.732 = 346.4