Angle of Depression: Definition, Examples, Chart, and Practice

What is an angle of depression?

An angle of depression is an angle measured downward from a horizontal line.

It is used when someone looks down from a higher place to an object below.

The horizontal line starts at the observer. The line of sight goes downward to the object.

Angle of depression rule

Use this rule when a problem says an observer is looking downward.

The angle of depression is between the horizontal line and the downward line of sight.

It is not measured from the vertical wall. It is measured from the horizontal reference line.

Angle of depression chart

This chart shows the parts of a common angle-of-depression diagram.

The right triangle is often made from height, horizontal distance, and the line of sight.

The height and horizontal distance meet at a right angle, which is why the triangle setup works.

Angle of depression and right triangles

Many angle-of-depression problems become right-triangle problems.

The vertical height is one leg, like the perpendicular height in altitude of a triangle problems. The horizontal distance is the other leg.

The line of sight is usually the hypotenuse.

Worked example

Problem: A person is 40 meters above the ground and sees a car 80 meters away horizontally. What is the angle of depression?

Step 1: Draw a right triangle. The opposite side is 40 and the adjacent side is 80.

Step 2: Use tangent: tan(angle) = opposite / adjacent = 40 / 80.

Step 3: tan(angle) = 0.5, so angle ≈ 26.6°.

Answer: The angle of depression is about 26.6°.

Angle of depression vs angle of elevation

Angle of depression is measured downward from a horizontal line.

Angle of elevation is measured upward from a horizontal line.

When the two horizontal lines are parallel, the angle of depression and the angle of elevation can be equal Z angles, or alternate interior angles.

Common mistakes

Do not measure the angle from the vertical wall. Use the horizontal line.

Do not confuse the line of sight with the horizontal distance.

Do not use tangent unless you have or need the opposite and adjacent sides. Choose the trigonometry ratio that matches the given information.

Quick practice

1. An angle of depression is measured downward from a horizontal line.

2. If height is 30 and horizontal distance is 30, tan(angle) = 1, so the angle is 45°.

3. If the observer looks upward, the problem uses an angle of elevation, not depression.

4. The vertical height and horizontal distance form a right angle.