question_answer

If the angle of elevation of a cloud from a point P which is 25 m above a lake be \[30{}^\circ \] and the angle of depression of reflection of the cloud in the lake from P be \[60{}^\circ \], then the height of the cloud (in metres) from the surface of the lake is [JEE Main Online Paper Held On 12-Jan-2019 Evening]

A) 50                                

B) 45   

C) 60                                

D)   42

Correct Answer: A

Solution :

In \[\Delta PAB,\]\[\tan {{30}^{o}}=\frac{x}{y}\Rightarrow y=\sqrt{3}x\]            ?(i) In\[\Delta PBC,\]\[\tan {{60}^{o}}=\frac{25+x+25}{y}\] \[\Rightarrow \]\[\sqrt{3}y=50+x\]\[\Rightarrow \]\[3x=50+x\][Using (i)] \[\Rightarrow \]\[x=25\] \[\therefore \]Height of cloud from the surface of the lake\[=25+25=50\text{ }m\]