What is the difference between Vertical Angles and Angle of Depression?

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In mathematics, the angle of depression and vertical angle are two different concepts. But both are critical points in trigonometry and help to do calculations of unknown angles, sides, and distances.

In this article, you will learn the difference between the angle of depression and the vertical angle. But before learning their difference, let’s discuss what vertical angles are.

What are Vertical Angles?

When two lines cross at a place in such a way that four angles are generated. These angles are directly opposed and measure the same. These four angles are known as vertical angles if they are equal and opposing to each other without sharing any sides.

Vertical angles are always congruent, which means that they are equal in measure and oppose each other. For example, when two lines AB and EF intersect each other at their common point O, such that:

The measure of angle between A and E is equal to the measure of angle between B and F.

These four angles in the above figure, which are equal to their adjacent angles, known as vertical angles. Vertical angle calculator helps you to find the adjacent angles. And these angles are calculated by using congruent and supplementary theorems.

What is the angle of depression? 

The angle of depression is an angle between the horizontal line and the light of sight of an observer. When you look down at an object, this angle is formed between your line of sight and the horizontal distance between you and the object.

In trigonometry, the angle of depression measures an unknown height or distance between two objects. The horizontal line may refer to the base, and the height may refer to the perpendicular of a triangle. Therefore, it is used to solve many triangular problems.

Angle of depression calculator works fine to calculate angle of depression using the trigonometric function tangent, which is a triangle’s ratio of base and hypotenuse. The formula to calculate the angle between the line of sight of the observer and the object is as follows:

Difference between angle of depression and vertical angle

The angle of depression and vertical angle are totally different from each other. But they have many applications in mathematics along with engineering and science. The major differences between angle of depression and vertical angles are given in the following difference table.

Vertical Angle	Angle of Depression
These angles are formed when two lines intersect at a common point, which is known as the vertex.	It is formed between the line of sight of an observer and the horizontal distance from the object.
There is no line of sight in vertical angles. But it involves the same measure of adjacent angles.	The line of sight is at a height from the observer i.e. it is in the downward direction.
Vertical angles can be supplementary and complementary as well.	Angle of depression is neither complementary nor supplementary.
Two adjacent angles are equal in measure and oppose each other. Therefore, they are always congruent.	The angle of depression does not satisfy the congruence theorem.
We can calculate an unknown angle by using the supplementary theorem.	It uses trigonometric ratio tangent to calculate unknown side or angle in triangles.

Conclusion

The vertical angles and angles of depression are two completely different concepts but we have one online calculator for both of them.

But they follow the same congruence theorem such that the angle of depression and elevation are congruent. And vertical angles are also congruent. The angle of depression is formed between the line of sight and the distance between the object.

At the same time, the vertical angles are created by the intersection of two straight lines at a common point. But both concepts are essential in trigonometry, which helps find the unknown angle of the side of a triangle.  

FAQ’s

What is the angle of the depression formula?

The angle of depression formula is used to calculate the unknown angle or side of a triangle. This formula is:

Where, the horizontal is the distance between the line of sight and the object.

Do vertical angles equal 90?

Yes, the vertical angles can be 90 degrees. Such angles can be formed when two straight lines intersect each other at right angles. According to the supplementary theorem, two neighbouring angles add up to 180 degrees.

What is vertical and horizontal?

Vertical and horizontal are two terms that describe direction. Horizontal describes the direction across the ground and the vertical line describes upward direction. These vertical and horizontal lines make a coordinate system together.

Are vertical angles perpendicular?

The vertical angles are always congruent. They can be perpendicular if two straight lines intersect each other at right angles. The axis of the plane (xy-coordinates) is an example of perpendicular lines.

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