Angle of Depression

Definition

As an observer looks downward at an object, an angle of depression is formed. This angle forms between a line that is parallel to the observer’s eye and the line of sight. 

Formula

The formula for angle of depression is the same as the basic trigonometric ratio formulas. We can easily find the angle of depression by using trigonometric ratio formulas.

\sin\theta=\frac{opp\;}{Hypotenous}.

\cos\theta=\frac{adj\;}{Hypotenous}.

\tan\theta=\frac{opp\;}{adj}.

The Angle of Depression in a Triangle

The point of depression forms at the top of the perpendicular line segment of a right-angled triangle. We find its alternate angle inside the triangle using the alternate interior angles theorem, as it originally lies outside the triangle. When an observer is standing at point A and looks down at point C, the angle of depression ‘a’ is formed with respect to the horizontal axis AD, as shown in the following image. However,  ∠DAC =  ∠ACB (using alternate angles theorem). As a result, in the triangle ABC, the depression angle is ∠ACB, which can be used to find the missing side of the triangle. Both the angle of depression and the angle of elevations are important for trigonometric operation.

Angle of Elevation

Definition

The angle of elevation is just opposite to the angle of depression. And the angle of depression is equal to the angle of elevation.

In order to determine the angle of elevation, you adjust the setting so that the observer looks above the object from a lower level. From the observer’s eye level, a horizontal line is drawn from the object to the line of sight (like the angle of depression). As the name implies, the angle of elevation is the distance between the horizontal line and the line of sight. 

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Azhar Ali

Azhar Ali

Mathematician and Blogger.

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