Angle Of Depression - Vedantu

The concept of angle of depression plays a key role in mathematics, especially in trigonometry, and is widely useful for solving problems related to heights and distances. This concept is regularly asked in school exams, Olympiads, and real-life contexts like aviation, architecture, and navigation.

What Is Angle of Depression?

The angle of depression is defined as the angle formed between a horizontal line from the observer’s eye and the line of sight when the observer looks downward at an object. You’ll find the angle of depression applied in areas such as trigonometry word problems, navigation, and geometry in daily life.

Key Formula for Angle of Depression

Here’s the standard formula to find the angle of depression using trigonometric ratios in a right-angled triangle:

tan θ = Opposite Side / Adjacent Side or, if the height (h) and horizontal distance (d) are given:

tan(angle of depression) = Height / Distance

Cross-Disciplinary Usage

The angle of depression is not only important in Maths but also plays an important role in Physics (projectile motion, navigation), Computer Science (graphics), and even logical reasoning. Students preparing for exams like JEE, NEET, or board tests often encounter angle of depression problems in various question forms.

Step-by-Step Illustration

1. Let’s solve this angle of depression example: A person stands on top of a tower 40 m high and notices a car on the ground at a horizontal distance of 40 m from the base. What is the angle of depression to the car?

1. Draw a right-angled triangle where one side is the tower’s height (40 m) and the other is the horizontal distance (40 m). 2. Let θ be the angle of depression. 3. Use the formula: tan θ = Opposite / Adjacent = height / distance = 40/40 = 1 4. θ = arctan(1) = 45°

Final Answer: The angle of depression is 45°.

Difference: Angle of Depression vs Angle of Elevation

Feature	Angle of Depression	Angle of Elevation
Position of Observer	Above the object	Below the object
Direction of Sight	Downward	Upward
Formed With	Horizontal at observer’s eye	Horizontal at observer’s eye
Common Mistake	Mislabeling reference line	Using wrong horizontal

Speed Trick or Vedic Shortcut

An easy way to remember: The angle of depression from a high point to an object below is equal to the angle of elevation from the object below up to the observer (alternate interior angles!). This helps you solve quickly without redrawing all triangles.

Exam Tip: Always draw the horizontal from the observer’s eye first. Then mark the angle from this line down to the object’s line of sight.

Try These Yourself

• If a person on a bridge 25 m above water sees a boat at a distance of 100 m, what is the angle of depression?
• From the top of a lighthouse 80 m tall, a lifeguard spots a swimmer at a 200 m horizontal distance. What is the angle of depression?
• A pilot at 500 m altitude sees the runway at a depression angle of 30°. How far is the runway horizontally?

Frequent Errors and Misunderstandings

• Mixing up angle of depression with angle of elevation.
• Forgetting to use the horizontal from the observer’s eye (not the ground).
• Not drawing a clear diagram before solving.
• Using the wrong trigonometric ratio or mixing up height/distance in formula.

Relation to Other Concepts

The idea of angle of depression connects closely with the angle of elevation, right angle triangles, and trigonometric ratios. Mastering this helps when solving more advanced problems on height and distance in mathematics and science.

Classroom Tip

A quick way to remember the difference: If you look down at something, think “depression” (both start with D)! Vedantu’s teachers also suggest drawing a simple stick figure with a line across the eye and then an arrow down to the object—instantly shows the angle of depression direction.

We explored angle of depression—from definition, formula, solved example, common mistakes, and connections to other concepts and subjects. Continue practicing with Vedantu to become confident at solving angle of depression problems and boost your speed for any exam!

Also explore: Angle of Elevation | Trigonometry | Right Angle Triangle | Height and Distance