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A man on the top of a tower, standing on the sea shore, finds that a boat coming towards him takes 10 minutes for the angle of depression to change from 30° to 60°. How soon the boat reach the seashore?
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- 5 minutes
- 7 minutes
- 10 minutes
- 15 minutes
Correct Option: A
Let speed of boat = v metre/minute
Time taken to reach B from D = t minutes
∠ACB = 30°; ∠ADB = 60°
AB = Tower
In ∆ABC,
| tan 30° = | BC |
| ⇒ | = | √3 | vt + 10v |
| ⇒ AB = | √3 |
In ∆ABD,
| tan 60° = | BD |
| ⇒ √3 = | vt |
⇒ √3 vt = AB
| ⇒ √3vt = | √3 |
⇒ 3t = 10 + t
⇒ 2t = 10
⇒ t = 5 minutes
