Angle of Depression

The angle of depression is an important concept in trigonometry used to measure how we look downward from a higher point, while the angle of elevation is used when we look upward from a lower point. Both are commonly used to calculate the heights of buildings and towers as well as distances.

Table of Content 

• What is Angle of Depression
• Angle of Depression Formula
• Angle of Depression and Elevation Comparison
• Angle of Depression Examples

What is Angle of Depression

The angle of depression is the angle formed between the horizontal line (eye level) and the line of sight when looking downward at an object.

Angle of Depression Formula

The angle of depression is calculated using trigonometric ratios based on a right triangle formed between the observer, the object, and the ground. The most commonly used formula is:

tan⁡θ=HeightDistance

 

Here, θrepresents the angle of depression, Height is the vertical distance between the observer and the object, and Distance is the horizontal distance between them.

In some cases, other trigonometric ratios like sine and cosine can also be used depending on the given values:

• sinθ = Height / Hypotenuse

• cosθ = Distance / Hypotenuse

Angle of Depression and Elevation Comparison

The angle of depression and the angle of elevation are important concepts in trigonometry used to calculate heights and distances. They are similar but differ based on the direction of viewing.

The angle of depression is equal to the angle of elevation when measured from the same horizontal line because they are alternate interior angles.

Angle of Depression Examples

Example 1

A building is 20 m high. The distance of a car from the base is 20 m. Find the angle of depression.

Solution: