A) \[50(\sqrt{3}-1)m\]
B) \[50\sqrt{3}m\]
C) \[50(\sqrt{3}+1)m\]
D) \[\frac{100}{\sqrt{3}-1}m\]
Correct Answer: A
Solution :
Here height of tree\[=AB\] In\[\Delta APB\] \[\tan {{30}^{o}}=\frac{AB}{BP}\Rightarrow \frac{1}{\sqrt{3}}=\frac{AB}{x}\] or \[x=\sqrt{3}AB\] ? (i) In \[\Delta AQB,\,\,\tan {{45}^{o}}=\frac{AB}{BQ}\] \[\Rightarrow \] \[\frac{AB}{100-x}=1\] \[\Rightarrow \] \[x=100-AB\] ? (ii) So from (i) and (ii) \[\sqrt{3}AB=100-AB\] \[\Rightarrow \] \[AB\left( \sqrt{3}+1 \right)=100\] \[\Rightarrow \] \[AB=\frac{100}{\sqrt{3}+1}\times \frac{\sqrt{3}-1}{\sqrt{3}-1}\] \[=50(\sqrt{3}-1)\] \[\therefore \]Height of tree \[=50(\sqrt{3}-1)\]metre.You need to login to perform this action.
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