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)
Answer & explanation
Correct answer: option 3
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