question_answer

The angle of elevation of the top of a tower at point on the ground is\[{{30}^{o}}\]. If on walking 20 metres toward the tower, the angle of elevation become\[{{60}^{o}}\], then the height of the tower is [MNR 1975; IIT 1967]

A) 10 metre

B) \[\frac{10}{\sqrt{3}}metre\]

C) \[10\sqrt{3}metre\]

D) None of these

Correct Answer: C

Solution :

 \[OA=h\,\cot {{60}^{o}},\,OB=h\cot {{30}^{o}}\], \[R=\frac{abc}{4\Delta }\] \[\Rightarrow \]  \[h=\frac{20}{\left( \sqrt{3}-\frac{1}{\sqrt{3}} \right)}=\frac{20\sqrt{3}}{2}=10\sqrt{3}\].