question_answer

A man is at a height of 100 m. He sees a car which makes an angle of \[\text{/6}\] with mans position. If the car moves to a point where angle is \[\text{/3}\] what is the distance moved by it?

A)  \[\left( \frac{100}{\sqrt{3}} \right)\text{m}\]    

B)         \[(200\sqrt{3})\text{m}\]             

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

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

Correct Answer: C

Solution :

In \[\Delta \,ABC\] \[\tan 60{}^\circ =\frac{100}{x}\] \[\Rightarrow \]               \[x=\frac{100}{\sqrt{3}}\]                                             ?(i) In \[\Delta \,ABD\] \[\tan 30{}^\circ =\frac{100}{x+y}\] \[\Rightarrow \]               \[x+y=100\sqrt{3}\] \[\Rightarrow \]               \[y=100\sqrt{3}-\frac{100}{\sqrt{3}}\]    from (i)     \[=\frac{200}{\sqrt{3}}m\]