A man is watching from the top of a tower a boat speeding away from the tower The angle of depressio...........

Quantitative Aptitude ( CCS) Trignometry

A man is watching from the top of a tower, a boat speeding away from the tower. The angle of depression from the top of the tower to the boat is 60⁰ when the boat is 80m from the tower. After 10 seconds, the angle of depression becomes 30⁰. What is the speed of the boat? (Assume that the boat is running in still water).

20 m/sec

10 m/sec

16 m/sec

18 m/sec

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Explanation:

Let AB is the tower and boat is at points C and D when the angles of depression are 60⁰ and 30⁰ respectively
Height & Distances
In ΔABC,
tan 60⁰= AB/AC
⇒ √3 = AB/80
⇒ AB = 80√3m
Again in ΔBAD,
tan 30⁰ = AB/AD
⇒ 1/√3 = 80√3/AD
⇒ AD = 80√3 × √3 = 240m
∴ CD = 240 – 80 = 160m
The boat took 10 seconds to cover 160m
∴ The speed of the boat = 160/10 = 16m/s