question_answer

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

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

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

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

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

Correct Answer: C

Solution :

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