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From a cliff 120 m above the shore of a sea, the angle of depression of a ship is 60°. Find the distance from the ship to a point on the shore directly below the observer.
  • a)
    120√2 m
  • b)
    100√3 m
  • c)
    33√3 m
  • d)
    40√3 m
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
From a cliff 120 m above the shore of a sea, the angle of depression o...

From the diagram,
AB = height of the cliff = 120 m
Angle of depression = ∠ CAE = 60°
BC = Distance of the ship to the bottom of the cliff
∴ ∠ CAB = 90° - 60° = 30°
From ΔABC
tan ∠CAB = perpendicular/Base
⇒ tan 30° = BC/AB
⇒ 1/√3 = BC/120
⇒ BC = 120/√3 m
⇒ BC = 120√3/3 m = 40√3 m
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