A) \[\left( \frac{\sqrt{3}-1}{\sqrt{3}+1} \right)60\,\,m\]
B) \[\left( \frac{\sqrt{3}+1}{\sqrt{3}-1} \right)60\,\,m\]
C) \[\left( \frac{\sqrt{3}+1}{\sqrt{3}-1} \right)m\]
D) None of these
Correct Answer: B
Solution :
Let \[OA\] be the light house and \[B\] be the position of boat. It is given that\[LOBA=LABL={{15}^{o}}\] Now,\[\tan {{15}^{o}}=\frac{OA}{OB}\] \[\Rightarrow \] \[OB=OA\cdot \cot {{15}^{o}}\] \[\Rightarrow \] \[OB=60\cdot \cot ({{45}^{o}}-{{30}^{o}})\] \[=60\left( \frac{\cot {{45}^{o}}\cdot \cot {{30}^{o}}+1}{\cot {{30}^{o}}-\cot {{45}^{o}}} \right)=60\left( \frac{\sqrt{3}+1}{\sqrt{3}-1} \right)m\].You need to login to perform this action.
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