Angle of Depression Calculator

Understanding angles in real life can be tricky, especially when it comes to heights and distances. The Angle of Depression Calculator makes it simple by using trigonometric formulas to calculate the angle of depression, elevation, horizontal distance, or slant distance. Whether you are a student, engineer, or just curious about geometry, this tool helps you get fast and accurate results with clear steps.

What is the Angle of Depression?

The angle of depression is the angle formed when an observer looks downward from a horizontal line of sight to an object below. Imagine standing on top of a building and looking at a car parked on the road. The angle between your straight horizontal eye level and the line of sight to the car is the angle of depression.

Interestingly, the angle of depression from the top equals the angle of elevation from the bottom when measured correctly. This relationship is widely used in trigonometry and real-life applications such as aviation, architecture, surveying, and navigation.

Angle of Depression Formula

The angle of depression can be calculated using basic trigonometry. If you know the height (h) and horizontal distance (b), the formula is:

θ = arctan(h / b)

If the angle θ is already known, we can find other distances:

Horizontal distance (b) = h / tan(θ)

Slant distance (d) = h / sin(θ)

Here:

• θ = angle of depression
• h = vertical height
• b = horizontal distance
• d = slant or line-of-sight distance

How to Use the Angle of Depression Calculator

1. Enter the height of the observer or object.
2. Choose the unit of measurement (meters, feet, kilometers, etc.).
3. Depending on your need, enter either the horizontal distance or the angle.
4. Select the mode: Find angle, find horizontal distance, or find slant distance.
5. Click calculate to get results instantly in both radians and degrees, along with the line-of-sight distance.

The calculator also shows a summary of your inputs and results so you can clearly understand each step.

Angle of Depression Examples with Solutions

Example 1: Find the angle of depression

A tower is 50 meters tall, and the horizontal distance to a car is 120 meters.

θ = arctan(h / b)

θ = arctan(50 / 120)

θ = arctan(0.4167)

θ ≈ 22.62°

So, the angle of depression is about 22.62 degrees.

Example 2: Find horizontal distance

A lighthouse is 30 meters tall, and the angle of depression to a boat is 15°.

b = h / tan(θ)

b = 30 / tan(15°)

b ≈ 112.04 meters

The boat is about 112 meters away from the lighthouse base.

Angle of Depression vs. Angle of Elevation

• Angle of Depression: When the observer looks downward.
• Angle of Elevation: When the observer looks upward from the ground toward an object above.

Both are measured from the horizontal line, and they are equal in corresponding situations.

Final Verdict

The Angle of Depression Calculator is an easy-to-use online tool that saves time and prevents calculation mistakes. With simple inputs, it shows you not only the angle but also the slant and horizontal distances. Students preparing for exams, professionals in construction, or anyone dealing with right-angle triangle problems can rely on this calculator for quick and accurate results.

FAQs

How do I find the angle of depression with 2 sides?

You use the formula θ = arctan(height / horizontal distance).

What is the difference between angle of depression and elevation?

Depression is looking downward, elevation is looking upward, both measured from the horizontal line.

Can I calculate angle of elevation with this calculator?

Yes, the same formulas apply because angle of elevation and depression are equal in right triangles.

Is this calculator accurate for real-world use?

Yes, it uses exact trigonometric functions and works with different units like meters, feet, miles, and kilometers.

Where is the angle of depression used in real life?

It is used in navigation, aviation, construction, surveying, and physics problems.