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Subject - Mathematics:

General

MCQ - 376-9108

Question:

The angle of depression of an object from a 60-m-high tower is 30˚. The Distance of the object from the tower is

  1. 20√ 3 m
  2. 60√ 3 m
  3. 40√ 3 m
  4. 60√ 3 m

Correct Answer: C

Explanation:

2 -88192768

Let the Distance of the object from the tower be x meters.
∴ BC = x m
Given –
height of tower = AB = 60 m
Angle of depression = ∠ DAC = 30°
∴ ∠ BCA = ∠ DAC = 30°
[∵ When two ‖ lines are intersected by a third line then the Alternate interior angles will be equal.]
Now, In Δ ABC
tan 30° = AB/BC = 60/x [∵ tan θ = perpendicular/base]
⇒ 1/√3 = 60/x
∴ x = 60√3 meters

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