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Angle of depression

The angle of depression is the angle made by the line of sight with the horizontal when an object is seen below eye level.

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Student-friendly explanation

When you stand at a window, on a terrace, or on a bridge and look down at an object, your line of sight goes downward from the horizontal. The downward angle between the horizontal line at your eye and the slant line to the object is called the angle of depression. In diagrams, it is often equal to the angle of elevation from the lower point because of alternate interior angle reasoning on parallel horizontals.

How to write this in exams

  1. 1

    Start with the exact idea

    The angle of depression is the angle made by the line of sight with the horizontal when an object is seen below eye level.

  2. 2

    Then show how to use it

    1. Find the observer at the higher point. 2. Draw the horizontal through the eye. 3. Draw the downward line of sight. 4. Measure the angle between the horizontal and the downward line. 5. Name it as angle of depression.

  3. 3

    Add one concrete example

    A person standing on a cliff looks down at a boat in the sea. The angle between the horizontal through the person's eye and the line of sight to the boat is the angle of depression.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to measure from the vertical drop. That gives a different angle and breaks the standard trigonometry setup.

Definition

The angle of depression is the angle made by the line of sight with the horizontal when an object is seen below eye level.

Example

A person standing on a cliff looks down at a boat in the sea. The angle between the horizontal through the person's eye and the line of sight to the boat is the angle of depression.

Rule to remember

Angle of depression = angle between the horizontal through the observer and the downward line of sight.

Memory hook

Depression means going down, so the line of sight goes below the horizontal.

Examples and method

Worked example

From the top of a lighthouse, a guard looks down at a boat. The angle between the horizontal and the line of sight downward is the angle of depression, and it can be matched with the boat's angle of elevation in a parallel-line diagram.

Method to apply

1. Find the observer at the higher point. 2. Draw the horizontal through the eye. 3. Draw the downward line of sight. 4. Measure the angle between the horizontal and the downward line. 5. Name it as angle of depression.

Diagram support

Draw the observer on top, a horizontal line through the eye, and a slant line going downward to the object. Mark the angle at the top.

How CBSE asks it

Identify the angle of depression in a terrace, tower, or bridge diagram, or use it to form an equation in a height-distance problem.

Avoid common mistakes

Common confusion

Students often measure the angle from the vertical drop line or from the ground, which gives the wrong angle.

Common wrong answer

A common wrong answer is to measure from the vertical drop. That gives a different angle and breaks the standard trigonometry setup.

Exam tip

First draw the horizontal at the observer's eye level. For depression, the line of sight goes downward below that line.

Quick check

A person on a terrace looks down at a car on the road. Which angle is formed at the observer's eye?

It is the angle of depression, because the object is below the observer's eye level and the line of sight is below the horizontal.

Study the angle of depression diagram carefully

Use the labelled diagram to keep angle of depression clear in short answers and revision.

What this diagram makes clear

This diagram keeps the labels and direction of angle of depression in the right order.

Where this helps in exams

Use this for labelled diagram work and short exam answers on angle of depression.

Revision cue

Revise angle of depression through the labels before writing the answer.

Answer writing and exam use

1-mark answer

The angle of depression is the angle made by the line of sight with the horizontal when an object is seen below eye level.

2-mark answer

The angle of depression is the angle made by the line of sight with the horizontal when an object is seen below eye level. Angle of depression = angle between the horizontal through the observer and the downward line of sight. A person standing on a cliff looks down at a boat in the sea. The angle between the horizontal through the person's eye and the line of sight to the boat is the angle of depression.

3-mark answer

When you stand at a window, on a terrace, or on a bridge and look down at an object, your line of sight goes downward from the horizontal. The downward angle between the horizontal line at your eye and the slant line to the object is called the angle of depression. In diagrams, it is often equal to the angle of elevation from the lower point because of alternate interior angle reasoning on parallel horizontals. Angle of depression = angle between the horizontal through the observer and the downward line of sight. From the top of a lighthouse, a guard looks down at a boat. The angle between the horizontal and the line of sight downward is the angle of depression, and it can be matched with the boat's angle of elevation in a parallel-line diagram. Identify the angle of depression in a terrace, tower, or bridge diagram, or use it to form an equation in a height-distance problem. A common wrong answer is to measure from the vertical drop. That gives a different angle and breaks the standard trigonometry setup.
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