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