A) \[25\sqrt{3}m\]
B) \[25\,\,m\]
C) \[25\sqrt{4}m\]
D) \[\frac{25}{\sqrt{3}}\,\,m\]
Correct Answer: A
Solution :
Let\[PQ=h\]be the height of chimney. \[A\]and\[B\]are the two points 50 m apart. In\[\Delta \,\,APQ\], \[\tan {{30}^{o}}=\frac{h}{AP}\] \[AP=h\cot {{30}^{o}}\] ... (i) and in\[\Delta \,\,QBP\], \[\tan {{60}^{o}}=\frac{h}{BP}\] \[BP=h\cot {{60}^{o}}\] ... (ii) \[\because \] \[AP-BP=50\] \[\therefore \] \[h(\cot {{30}^{o}}-\cot {{60}^{o}})=50\] \[\Rightarrow \] \[h=\frac{50}{\left( \sqrt{3}-\frac{1}{\sqrt{3}} \right)}=\frac{50\sqrt{3}}{3-1}\] \[=\frac{50\sqrt{3}}{2}=25\sqrt{3}m\]You need to login to perform this action.
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