question_answer

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,     \[\frac{AB}{OB}=\tan 30{}^\circ \]

\[\Rightarrow \]   \[AB=(20+BC)\,\,\tan 30{}^\circ \]

\[\Rightarrow \]   \[AB=(20+AB)\frac{1}{\sqrt{3}}\]

\[\Rightarrow \] \[\sqrt{3}\,AB-AB=20\]

\[\Rightarrow \]   \[AB=\frac{20}{\sqrt{3}-1}=\frac{20\,(\sqrt{3}+1)}{2}\]

\[=10\,(\sqrt{3}+1)\]