Angle Of Elevation Vs Angle Of Depression

Angle of Elevation

The angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line. It is formed when an observer looks upwards. Suppose you are standing at the terrace of a building and looking upwards at the sky or at the sun or moon. The angle thus formed between your height from the ground level and the line of sight formed is called the angle of elevation.

1.	Angle of Elevation Definition
2.	Angle of Elevation Formula
3.	Angle of Elevation Vs Angle of Depression
4.	FAQS on Angle of Elevation

Angle of Elevation Definition

The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation". It is always at a height that is greater than the height of the observer. The opposite of the angle of elevation is the angle of depression which is formed when an observer looks downwards. It is important to learn about the angle of elevation and depression while studying heights and distances in trigonometry. The three general words associated with the angle of elevation are angles, horizontal lines, and line of sight.

Let the observer at 'O' is observing an object that is at 'A'. Then the horizontal line is OB and the line of sight is OA. Then the angle formed between OA and OB which is angle AOB is the angle of elevation.

Angle of Elevation Formula

The angle of elevation formula isno different from the formulae of trigonometric ratios. With the help of the formulae given below, we can find the angle of elevation depending on which two sides of the triangle are known. For example, if we have to find the angle of elevation when the height of the object from the horizontal line and the length of the line of sight are known, we can use the sine formula.

For example, to calculate the angle of elevation for an object at the distance of 10 units from the horizontal line (y=10) and 12 units from the observer w.r.t. the horizontal line (x=12), we write, tan θ = 10/12, which can be reduced to tan θ = 5/6. Therefore, the value of θ obtained is tan-1 (5/6). This is the required angle of elevation.

Angle of Elevation Vs Angle of Depression

The angle of elevation and angle of depression are opposites of each other. In an angle of elevation, the object is placed above the observer, while in the case of the angle of depression, it is placed below 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 elevation and depression from the table given below.

Angle of Elevation	Angle of Depression
It is formed when an object is placed above the observer.	It is formed when an object is placed below the observer's eye level.
Also known as upwards angle.	Also known as downwards angle.
The horizontal line is below the object.	The horizontal line is above the object.

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

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