question_answer

    From an aeroplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the sameside of the aeroplane are observed to be\[30{}^\circ \]and\[60{}^\circ \]respectively The height at which the aeroplane is flying in km is

A)  \[\frac{4}{\sqrt{3}}\]                                    

B)  \[\frac{\sqrt{3}}{2}\]

C)  \[\frac{2}{\sqrt{3}}\]                                    

D)  \[2\]

Correct Answer: B

Solution :

                Let the distance of two consecutive stones are\[x,\text{ }x+1\]. In\[\Delta BCD,\]                 \[\tan 60{}^\circ =\frac{h}{x}\] \[\Rightarrow \]               \[x=\frac{h}{\sqrt{3}}\]                                 ??.(i) In\[\Delta ABC,\]                 \[\tan 30{}^\circ =\frac{h}{x+1}\] \[\Rightarrow \]               \[\frac{1}{\sqrt{3}}=\frac{h}{x+1}\] \[\Rightarrow \]               \[\frac{h}{\sqrt{3}}+1=\sqrt{3}h\]                                  [from(i)] \[\Rightarrow \]               \[\frac{2h}{\sqrt{3}}=1\] \[\Rightarrow \]               \[h=\frac{\sqrt{3}}{2}km\]