Introduction
The topic of angle of depression and elevation is an important concept in trigonometry and is widely used in fields such as surveying, navigation, and construction. Understanding the difference between these two concepts is crucial for accurately measuring and calculating distances, heights, and angles in real-world scenarios.
Angle of depression is the angle between the horizontal and a line of sight from a higher point to a lower point. For example, an observer standing on a hill looking down at an object below would measure the angle of depression.
On the other hand, angle of elevation is the angle between the horizontal and a line of sight from a lower point to a higher point. For example, an observer standing at the base of a building looking up at the top of the building would measure the angle of elevation.
Both angles of depression and elevation play an important role in determining distances, heights and angles in real-world scenarios. For example, in surveying, angles of depression and elevation are used to measure the height of a building or a tower. In navigation, angles of depression and elevation are used to determine the position of a ship or an aircraft. And in construction, angles of depression and elevation are used to design and construct safe and stable structures.
In this post, we will take a closer look at the difference between angle of elevation and angle of depression, how to measure them, and their real-life applications. By the end of the post, you will have a better understanding of how these concepts are used in everyday life and how they can be applied in various fields.
Related: Understand angle of depression in triangles
Definition of Angle of Depression and Elevation
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.
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.
Real-Life applications
Let's look at some real life applications of angle of depression and elevation.
Example no. 1
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
You can also use angle of elevation and depression calculator for solving it online.
Example no. 2
Another example of where angle of depression and elevation are used in real-life scenarios is in the field of aviation. Pilots use angles of depression and elevation to determine the position and altitude of an aircraft.
For example, when a pilot is flying at a certain altitude and wants to determine the distance to the ground below, they can measure the angle of depression from the aircraft to the ground. By using trigonometry, the pilot can then calculate the distance from the aircraft to the ground based on the angle of depression.
Similarly, when a pilot wants to determine the altitude of an aircraft, they can measure the angle of elevation from the ground to the aircraft. By using trigonometry, the pilot can then calculate the altitude of the aircraft based on the angle of elevation.
This allows pilots to navigate safely, avoiding obstacles, and maintaining a safe distance from the ground and other aircrafts.
Additionally, Air traffic controllers also use angles of depression and elevation to keep track of the positions of all the aircrafts in their airspace and ensure safe separation between them.
Now that we've discussed few examples of angle of depression and elevation, let's discuss about key differences both have.
Difference between angle of elevation and angle of 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 angle of elevation vs angle of depression 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. |
| It 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. |
| It is measured in a downward direction, with 0 degrees indicating parallel to the ground and 90 degrees indicating perpendicular to the ground. |
It is measured in an upward direction, with 0 degrees indicating parallel to the ground and 90 degrees indicating perpendicular to the ground. |
| It is used to calculate the distance from a higher point to a lower point. |
It is used to calculate the distance from a lower point to a higher point. |
| It is complementary to the angle of elevation (the sum of the two angles is always 90 degrees). |
It is complementary to the angle of depression (the sum of the two angles is always 90 degrees). |
| It is commonly used in navigation, surveying and construction. |
It is commonly used in navigation, surveying and construction. |
| It is used to calculate the height of an object below the observer. |
It is used to calculate the height of an object above the observer. |
Conclusion
Angle of depression and angle of elevation are important concepts in trigonometry that are widely used in fields such as surveying, navigation, and construction. The main difference between the two is that angle of depression is the angle between the horizontal and a line of sight from a higher point to a lower point, while angle of elevation is the angle between the horizontal and a line of sight from a lower point to a higher point. Both angles are complementary, with the sum of the two angles being 90 degrees.
Throughout this post, we covered angle of depression definition, angle of elevation and depression examples, how to measure them, and their real-life applications. We also discussed angle of elevation vs depression between the two concepts and provided examples to help illustrate the concepts.
We hope this post has helped you better understand the concepts of angle of depression vs angle of elevation, and their importance in various fields. If you have any additional questions or would like more information on the topic, please feel free to ask.
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 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)
How to measure angle of elevation in real life?
Angle of elevation can be measured using a protractor or clinometer. Place the device at eye level and aim it at the object to get the angle reading.