SSC
Quantitative Aptitude
Trigonometry
Question Bank
Trigonometry (I)
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 \[H=h\cot x-h\]