CAT Practice : Trigonometry

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Max and Min value of the given expression

Height and Distances

Q.9: A man standing on top of a tower sees a car coming towards the tower. If it takes 20 minutes for the angle of depression to change from 30° to 60°, what is the time remaining for the car to reach the tower?
1. 20√3 minutes
2. 10 minutes
3. 10√3 minutes
4. 5 minutes

Choice B. 10 minutes

Detailed Solution

From the figure:-

tan 30° = $\frac{h}{(a+b)}$

tan 60° = $\frac{h}{b}$

$\frac{(a+b)}{√3} = b√3$

=) a + b = 3b

=) 2b = a

=) b = $\frac{a}{2}$

Now since the car takes 20 minutes to travel a distance

Time taken to travel b = $\frac{a}{2}$ distance =) $\frac{20}{2}$ = 10 minutes

Correct Answer: 10 minutes

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