A) \[400\sqrt{3}\,m\]
B) \[\frac{400}{\sqrt{3}}\,m\]
C) \[\frac{100}{\sqrt{3}}\,m\]
D) \[200\sqrt{3}\,m\]
Correct Answer: B
Solution :
Let PQ be the cliff and A and B be the points under Observations \[\therefore \] \[PQ=100\,m\] In right angled \[\Delta \,APQ,\] \[\frac{AQ}{PQ}=\cot {{30}^{o}}\] \[\Rightarrow \] \[AQ=PQ.\sqrt{3}\] \[\Rightarrow \] \[AQ=100\sqrt{3}\] ?(i) In right angled \[\Delta BPQ,\] \[\frac{BQ}{PQ}=\cot {{60}^{o}}\] \[\Rightarrow \] \[BQ=\frac{100}{\sqrt{3}}\] ?(ii) Adding Eqs. (i) and (ii), we get \[AQ+BQ=100\left( \sqrt{3}+\frac{1}{\sqrt{3}} \right)\] \[\Rightarrow \] \[AB=100\frac{(3+1)}{\sqrt{3}}=\frac{400}{\sqrt{3}}m\]You need to login to perform this action.
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