JEE Main 12 Jan 2019 Evening Question 22
Question: 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]
Options:
A) 50
B) 45
C) 60
D) 42
Show Answer
Answer:
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=50m $
