question_answer

A man is height of\[100\,m\]. He sees a car which makes an angle of \[\frac{\pi }{6}\]with man's position. If the car moves at a point-where angle is\[\frac{\pi }{3},\] what is the distance moved by it?

A)  \[\left( \frac{400}{\sqrt{3}} \right)\,m\]          

B)  \[\left( 200\sqrt{3} \right)m\]

C)  \[\left( \frac{200}{\sqrt{3}} \right)\,m\]         

D)  \[\left( \frac{150}{\sqrt{3}} \right)\,m\]

Correct Answer: C

Solution :

In \[\Delta ABC,\]we have, \[\tan {{60}^{o}}=\frac{100}{x}\] \[\Rightarrow \] \[x=\frac{100}{\sqrt{3}}\] ?..(i) \[\Rightarrow \] \[x+y=100\sqrt{3}\] ?..(ii) Using equation (i) and (ii) become \[y=100\sqrt{3}-\frac{100}{\sqrt{3}}\] \[\Rightarrow \] \[y=\frac{100\times 3-100}{\sqrt{3}}=\frac{200}{\sqrt{3}}\,m\]