A) \[10\sqrt{3}\,m\]
B) \[\frac{10\sqrt{3}\,}{3}m\]
C) \[10(\sqrt{3}+1)m\]
D) \[10(\sqrt{3}-1)m\]
Correct Answer: A
Solution :
Let AB be the tree broken at point C, Let \[AC=x\text{ }m\]and \[CD=CB=y\text{ }m.\] Then, height of the tree \[=(x+y)m.\] Now, in right \[\Delta ADC,\] \[\frac{AC}{AD}=\tan {{30}^{o}}\Rightarrow \frac{x}{10}=\frac{1}{\sqrt{3}}\] \[\Rightarrow \] \[x=\frac{10}{\sqrt{3}}m\] And, \[\frac{AD}{CD}=\cos {{30}^{o}}\] \[\Rightarrow \] \[\frac{10}{y}=\frac{\sqrt{3}}{2}\Rightarrow y=\frac{20}{\sqrt{3}}m.\] \[\therefore \] Height of the tree \[=(x+y)\] \[=\left( \frac{10}{\sqrt{3}}+\frac{20}{\sqrt{3}} \right)=\left( \frac{30}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}} \right)=10\sqrt{3}m\]You need to login to perform this action.
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