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Difference between Angle of Depression and Elevation

When a man looks at an object at a lower level, the angle of depression is formed; when he looks at an object at an upper level, the angle elevation is formed. These are two basic concepts of trigonometry that help to solve many problems. We can find the unknown horizontal or vertical distance when the angle of depression or elevation is known.

What is the Angle of Depression?

The angle of depression is the angle between the vertical and horizontal lines where the line of sight is in the downward direction. For example, if a person is looking at an object in a downward direction, then the angle between the horizontal distance from the object and line of sight is the angle of depression.

The angle of depression depends on two factors: height and horizontal distance and it can be calculated by applying inverse tangent to the ratio of vertical distance and the horizontal distance as

θ = (vertical distance / horizontal distance)

Where the vertical distance may refer to the height at which the observer is standing and the horizontal distance may be the distance between the observer and the object.

What is the Angle of Elevation?

The angle of elevation is the opposite of the angle of depression. It is defined as the distance between an object and a person with the line of sight in an upward direction. For example, if a person is looking upward at an object, then the angle between the observer and the object is the angle of elevation.

The angle of elevation is the same in concept but opposite to the angle of depression. It is calculated by applying the inverse tangent to the ratio of horizontal distance and the vertical line of sight as

θ = (vertical distance / horizontal distance)

In the case of angle of elevation, the line of sight between the observer and the object is in upward direction. Difference between Angle of Elevation and Depression

In trigonometry the angle of elevation and depression are two main concepts that help to find the angle with vertical and horizontal lines. Moreover, unknown height and distance can also be calculated by these formulas. The main difference between angle of elevation and depression is that both are opposite to each other. Let us understand the difference between angle of depression and elevation with the given table.

Angle of Depression Angle of Elevation
The object is placed in a downward direction to the observer. The object is placed in an upward direction to the observer.
The line of sight is in downward direction. The line of sight is in an upward direction.
TIt is also known as the downward angle. It is also known as the upward angle.
The horizontal distance is taken below the observer. The vertical distance is taken above the observer.

Example

calculate angle of depression and elevation

A man is looking at a cat who is 12ft away from him. At the same time he looks at the flying aeroplane which is at horizontal distance 12ft from the man. If the height of the man is 6ft, find the angle of depression and elevation.

To calculate angle of depression,

h = 6ft

d = 12ft

Using the formula of angle of depression,

θ = 6 / 12

θ = 56.30o

To calculate angle of elevation,

θ = 12 / 6

θ = 63.43o

FAQ’s

What is an angle of elevation and depression?

The angle of elevation defined as the angle between the vertical and horizontal line with the line of sight is in upward direction. Whereas the angle of depression is defined as the angle between the vertical line of sight and the horizontal distance in downward direction.

What is the relationship between angle of elevation and angle of depression?

The angle of elevation and depression are opposite to each other when they are related to the same observer.

Is the angle of depression and elevation the same?

No, the angle of depression and elevation is not the same because they are in opposite directions.

What is the angle of elevation of the sun?

The angle of elevation of the sun from an observer's eye is 45o.

What is the formula of angle of elevation?

The formula of the angle of elevation is

θ = (horizontal distance / vertical distance)