question_answer

If the angle of elevation of a cloud from which is 25 m above a lake be \[35{}^\circ \] and the depression of reflection of the cloud in the P be \[60{}^\circ ,\] then the height of the cloud (in the surface of the lake is:

A) 60

B) 50

C) 45        

D) 42

Correct Answer: B

Solution :

\[\tan 30{}^\circ =\frac{x}{y}\]\[\Rightarrow \]\[y=\sqrt{3x}\]

\[\tan \,\,60{}^\circ =\frac{25+x+25}{y}\]

\[\Rightarrow \]   \[\sqrt{3y}=50+x\]    \[\Rightarrow \]\[3x=50+x\]       \[\Rightarrow \]          \[x=25\text{ }m\]

\[\therefore \] Height of cloud from surface

\[=25+25\]\[=50\text{ }m.\]