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 \[{{45}^{o}}\]respectively. The height of building is \[h\] metre Then the height of the chimney in metre, is:

A) \[h\cot x+h\]                 

B) \[h\cot x-h\]  

C) \[h\tan x-h\]      

D)        \[h\tan x+h\]

Correct Answer: B

Solution :

\[AB=\]Building \[=h\] metre \[AD=\]Chimney\[=y\] metre From\[ABCD\], \[\tan {{45}^{o}}=\frac{BD}{BC}\] \[\Rightarrow \]   \[1=\frac{h+y}{BC}\] \[\Rightarrow \]   \[BC=h+y\]                               ? (i) From\[\Delta ABC\],             \[\tan x=\frac{AB}{BC}\]             \[BC=h\cot x\]                           ?(ii) From equations (i) and (ii).             \[h+y=h\cot x\] \[\Rightarrow \]   \[y=(h\cot x-h)\]metre