question_answer

The angles of elevation of the top of a building and the top of the chimney on the roof of the building from a point on the ground are x and\[45{}^\circ \], respectively. The height of building is h m. Then, the height of the chimney is (in metre)

A) \[h\,\,\cot x+h\]

B) \[h\,\cot x-h\]

C) \[h\tan x-h\]

D) \[h\tan x+h\]

Correct Answer: B

Solution :

[b] Let the height of chimney by H m. In \[\Delta \Alpha \Beta C,\] \[\Rightarrow \]            \[\tan 45{}^\circ =\frac{H+h}{AB}\] \[1=\frac{H+h}{AB}\] \[\therefore \]      \[AB=H+h\] and in \[\Delta \Alpha \Beta D,\] \[\tan x=\frac{h}{AB}\] \[\therefore \]      \[AB=h\cot x\] On solving the Eqs. (i) and (ii), we get \[H=h\cot x-h\]