Angle Of Depression Problems

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If an observer is looking at an object located at a height lower than the observer, then the angle formed by the observer along the line of sight with the horizontal line is called the Angle of depression. Angle of depression can be evaluated by using the trigonometric functions like ‘sine’, ‘cos’ or ‘tan’ and calculating their values accordingly.

Example 1:  Evaluate the angle of depression if the observer standing on top of a building is at a height of 12m above the ground is looking at an object on the ground. The horizontal distance between the observer and the object is 24m.

Given height above the ground = 12m
Distance of the car from the observer = 24m
Let the angle of depression = θ
Then from the diagram, alternate angles are equal.
Hence the angle below ?OBA as shown is also = θ



Now in triangle OAB, tanθ= OA/AB = 12/24 = 1/2
Hence angle of depression, θ = tan-1(1/2) = 26.57°



 
Example 2: Find the angle of depression when an observer on a building at a height of 30m above the ground is looking at a car on the ground which is 60m away along the line of sight.

Given height above the ground = 30m

Distance of the car on the ground from the observer along the line of sight = 60m

Let the angle of depression = θ

Then, sinθ = Opposite side/Hypotenuse = 30/60 = 1/2
Hence angle of depression, θ = sin-1(1/2) = 30°.

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