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  4. A man from the top of a 50 metre high tower sees a car moving towards a tower at an angle of depression 30°. After sometime, the angle of depression is 60°. Then the distance travelled by the car during the time is

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Q. A man from the top of a 50 metre high tower sees a car moving towards a tower at an angle of depression $30°$. After sometime, the angle of depression is $60°$. Then the distance travelled by the car during the time is

COMEDKCOMEDK 2006Probability - Part 2

Solution:

In $\Delta \, ABC,$ we have $\tan 30° = \frac{50}{x+y} \frac{1}{\sqrt{3}} = \frac{50}{x+y} \, \, \, $...(i)
In $\Delta ABD,$ we have $ \tan 30° = \frac{50}{x+y}$
$\Rightarrow \sqrt{3} = \frac{50}{y} \Rightarrow y= \frac{50}{\sqrt{3} } \Rightarrow \frac{1}{\sqrt{3}} = \frac{50}{x+\frac{50}{\sqrt{3}}} $
$\Rightarrow \frac{1}{\sqrt{3}} = \frac{50\sqrt{3}}{\sqrt{3} x +50} \Rightarrow \sqrt{3} x +50 = 50 \times3$
$ \Rightarrow x = \frac{100}{\sqrt{3}} m\qquad$

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