Angle of Depression Definition

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Angle of depression is the angle formed by the observer’s eye with respect to the horizontal line. Angle of depression is only formed when the desired object is below the observer and the observer is looking down at the object. Angle of depression can be calculated by using the trigonometric functions and the given distances in a particular situation.

Example 1:  Evaluate the angle of depression if the observer who is at a height of 10m above the ground is looking at a car parked on the ground. The horizontal distance between the observer and the car is 15m.

Given height above the ground, OA = 10m
Distance of the car from the observer, AC = 15m
Let the angle of depression = θ
Then from the diagram, alternate angles are equal.
Hence the angle below L OCA as shown is also = θ

Now in triangle OAC, tanθ = OA/AC = 10/15 = 0.667

Hence angle of depression, θ = tan-1(0.667) = 33.7°

Example 2: If a person of height 6m is standing and is looking at a point on the ground 6m away. Find the person’s angle of depression.
Given height above the ground = 6m
Distance of the point on the ground from the person= 6m

Let the angle of depression = θ
Then, tanθ = Opposite side/Adjacent side = 6/6 = 1
Hence angle of depression, θ = tan-1(1) = 45°

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