# QA – Placement Quizzes | Trigonometry & Height and Distances | Question 9

A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man’s eye when at a distance of 60 meters from the tower. After 5 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?**(A)** 32 kmph**(B)** 36 kmph**(C)** 40 kmph**(D)** 44 kmph**Answer:** **(A)****Explanation:** Let the tower be PQ and the boat be at positions R and S when making angles of 45° and 30° respectively.

Given, PR = 60 m.

Now, PQ/PR = tan 45° = 1. So, PQ = PR = 60 m.

Again, PQ/PS = tan 30° = 1/√3. So, PS = 60 * √3 m = 103.92 m.

Distance covered in 5 seconds = 103.92 – 60 = 43.92 m.

Speed in kmph = (43.92/5) * (18/5) = 32 kmph (approximately)

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