Input data in **angle of depression calculator** to find the angle formed between the **horizontal line of sight** and the line of sight to an object located **below** the observer.

For example, a **lifeguard** in a tower spots a **swimmer in distress**. The **angle of depression** helps determine the **swimmer’s distance** from the **shore**, enabling a more **efficient rescue operation**.

## Angle of Depression Calculator

Height (m) | Distance (m) | Angle (degrees) | Angle (radians) |
---|---|---|---|

10 | 20 | 26.57° | 0.4636 rad |

50 | 30 | 59.04° | 1.0303 rad |

100 | 150 | 33.69° | 0.5880 rad |

75 | 80 | 43.15° | 0.7532 rad |

200 | 100 | 63.43° | 1.1071 rad |

**Conversion equation**: **Radians = Degrees × (π / 180)**

## Angle of Depression Formula

The formula is :

**tan(θ) = Height / Distance**

Where:

**θ**is the angle of depression**Height**is the vertical distance between the observer and the object**Distance**is the horizontal distance from the base of the observer’s position to the object

If a **drone operator** is flying a drone at **100 meters** altitude and spots a target **200 meters** away horizontally, the angle of depression would be:

**tan(θ) = 100 / 200 = 0.5****θ = arctan(0.5) ≈ 26.57°**

The formula for calculating the angle of depression is derived from **trigonometric principles**. In a **right-angled triangle** formed by the observer’s position, the object, and the ground, the angle of depression (θ) is given by:

## How to Find Distance in Angle of Depression?

To find the distance using the angle of depression, we rearrange the formula:

**Distance = Height / tan(θ)**

This calculation is particularly useful in scenarios where **direct measurement** is impractical or impossible.

Consider a situation where a **hiker** on a mountain ridge wants to estimate the distance to a lake below. If the hiker knows their elevation above the lake is **500 meters** and measures an angle of depression of **30°**, the distance to the lake would be:

**Distance = 500 / tan(30°) ≈ 866.03 meters**

## Can an Angle of Depression be 90 Degrees?

Theoretically, an angle of depression **can approach 90 degrees**, but it can never exactly reach it in practical scenarios.

A **90-degree angle of depression** would imply that the observer is directly above the object, with **no horizontal separation**.

In reality, even when looking straight down from a **tall structure** or **aircraft**, there’s always a slight deviation from 90 degrees due to factors like:

- The observer’s eye position relative to the edge of the structure
- The physical impossibility of positioning oneself exactly above a point on the ground

For example, a **skydiver** in free fall might experience an angle of depression very close to 90 degrees, but it would still be slightly less due to the **horizontal movement** caused by wind and the Earth’s rotation.

## How to Find the Angle of Depression in a Right Triangle

To find the angle of depression in a right triangle:

**Identify the known sides**: Usually, you’ll know the height (opposite side) and the horizontal distance (adjacent side).**Use the tangent function**: tan(θ) = Opposite / Adjacent**Calculate the inverse tangent (arctan)**to find the angle

For example, if you’re standing on a **30-meter tall building** and spot a car **40 meters** away from the base:

- Opposite (height) =
**30 meters** - Adjacent (distance) =
**40 meters** - tan(θ) = 30 / 40 =
**0.75** - θ = arctan(0.75) ≈
**36.87°**

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