A) \[50\sqrt{2}\,\,\text{m}\]
B) 100 m
C) \[100\,\,(\sqrt{3}-1)\,\,\text{m}\]
D) \[100\,\,(\sqrt{3}+1)\,\,\text{m}\]
Correct Answer: C
Solution :
Let the height of the incomplete piller be x m and the increasing height be PC = h m. |
In \[\Delta ABC,\] |
\[\tan 45{}^\circ =\frac{x}{100}\] |
\[\Rightarrow \] \[x=100\,\,\text{m}\] |
and in \[\Delta APB,\] |
\[\tan 60{}^\circ =\frac{x+h}{100}\] |
\[\Rightarrow \] \[x+h=100\sqrt{3}\] |
\[\Rightarrow \] \[h=100\sqrt{3}-x=100\sqrt{3}-100\] |
\[\Rightarrow \] \[h=100\,\,(\sqrt{3}-1)\,\,\text{m}\] |
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