A) \[50\,\,(\sqrt{3}-1)\,\,m\]
B) \[50\sqrt{3}\,\,\text{m}\]
C) \[50\,\,(\sqrt{3}+1)\,\,\text{m}\]
D) \[=(18\times 15\times 12)c{{m}^{3}}\]
Correct Answer: A
Solution :
Here, height of tree = AB |
In \[\Delta APB,\] |
\[\tan 30{}^\circ =\frac{AB}{BP}\Rightarrow \frac{1}{\sqrt{3}}=\frac{AB}{x}\] ?(i) |
In \[\Delta AQB,\]\[\tan 45{}^\circ =\frac{AB}{BQ}\] |
\[\frac{AB}{100-x}=1\] |
\[\Rightarrow \] \[x=100-AB\] ?(ii) |
So, from Eqs. (i) and (ii) |
\[\sqrt{3}AB=100-AB\] |
\[AB=\frac{100}{\sqrt{3}+1}\times \frac{\sqrt{3}-1}{\sqrt{3}-1}=50(\sqrt{3}-1)\] |
\[\therefore \] Height of tree \[=50\,\,(\sqrt{3}-1)\,\,\text{m}\] |
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