A Boat is being rowed away in still water, from a 210 metres high cliff at the speed of 3 km/hr. What is the approximate time taken for the angle of depression of the cliff at the boat to change from 60 deg. To 45 deg.?
Explanation:
When the boat was at C, the angle of depression = 60° ⇒ m∠ BAC = 30°
When the boat was at D, the angle of depression = 45° ⇒ m∠DAB = 45° ⇒ BD
= AB = 210 m
In ∆ABC, by theorem of 30° – 60° – 90°,
BC = 70√3 ≈ 121.1
DC ≈ 210 – 121.2 = 88.8 m
Speed of the boat = 3 km/ hr = 50 m/min
Time taken = 88.8/ 50 = 1.776 minutes
Hence, option (d).
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