If the angle of elevation of the sun changes from \[30{}^\circ \] to \[45{}^\circ ,\] then the length of the shadow of a pillar decreases by 20 m. The height of the pillar is [SSC (CPO) 2011] |
A) \[20\,(\sqrt{3}-1)m\]
B) \[20\,(\sqrt{3}+1)m\]
C) \[10\,(\sqrt{3}-1)m\]
D) \[10\,(\sqrt{3}+1)m\]
Correct Answer: D
Solution :
\[\frac{AB}{BC}=\tan 45{}^\circ \] |
\[\Rightarrow \] \[AB=BC\] |
Now, \[\frac{AB}{OB}=\tan 30{}^\circ \] |
\[\Rightarrow \] \[AB=(20+BC)\,\,\tan 30{}^\circ \] |
\[\Rightarrow \] \[AB=(20+AB)\frac{1}{\sqrt{3}}\] |
\[\Rightarrow \] \[\sqrt{3}\,AB-AB=20\] |
\[\Rightarrow \] \[AB=\frac{20}{\sqrt{3}-1}=\frac{20\,(\sqrt{3}+1)}{2}\] |
\[=10\,(\sqrt{3}+1)\] |
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