Angle Of Depression - Definition, Formula, Examples - Cuemath

Angle of Depression

The angle of depression is formed when an observer looks down at an object. It is the angle formed between the horizontal line which is straight to the observer's eye and the line of sight. Let us learn more about the angle of depression in this article.

1.	What is Angle of Depression?
2.	Angle of Depression Terminology
3.	Angle of Depression Formula
4.	Angle of Depression Vs Angle of Elevation
5.	Angle of Depression in a Triangle
6.	FAQs on Angle of Depression

What is Angle of Depression?

The angle of depression is "an angle formed between the horizontal line and the line of sight when an observer looks downwards at an object is known as an angle of depression". It measures the change of angle of our sight when we look down. Suppose you are standing in your kitchen and looking straight, and suddenly you spot an insect crawling on the floor. So, that immediate change in the angle of your sight from straight to downwards is the angle of depression.

Angle of Depression Terminology

The angle of depression involves the following terminology:

• Observer (the person who observes)
• Object (the object that is being observed by the observer)
• Horizontal line (a horizontal ray that starts from the observer)
• Line of sight (the line that connects the observer and the object)

The angle of depression is the angle between the horizontal line and the line of sight. In the following figure, the observer is at 'O' and the object is at 'B'. Let OA be the horizontal line and OB be the line of sight. So, the angle formed between these two, i.e angle AOB is the angle of depression.

Angle of Depression Formula

The formula for the angle of depression is the same as basic trigonometric ratios formulae. If any two sides of the right triangle formed are known, then we can easily find the required angle by using the angle of depression formulas, that are given below.

Angle of Depression Vs Angle of Elevation

The angle of depression and angle of elevation are opposites of each other. In the angle of depression, the object is placed below the observer, while in the case of the angle of elevation, it is placed above the observer. If you are standing at your terrace and looking at the sun, then the angle of elevation will be formed. On the other hand, if you will look at the dog standing on the road from your terrace, then the angle of depression will be formed. In both cases, we use trigonometry angles to find the heights and distances. Let us understand the difference between the angle of depression and elevation from the image given below.

In the above image, θ is the angle of elevation and α is the angle of depression.

Angle of Depression in a Triangle

In a right-angled triangle, the angle of depression is formed at the top of the perpendicular line segment. It is originally at the outside of the triangle, but we use the alternate interior angles theorem to find its alternate angle inside the triangle. For example, in the image given below, if an observer is standing at point A looking down at point C then the angle of depression 'a' is formed with respect to the horizontal axis AD. But, ∠DAC = ∠ACB (by using alternate angles theorem). So, now in the triangle, ABC, the angle of depression is ∠ACB which can be used to find measure the missing side of the triangle.

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