Definition
The Angle of Depression is the angle measured downward from a horizontal reference line (the horizontal ray) to the observer’s line of sight toward an object below them.
- How to read: “The angle of depression beta.”
- Meaning: Measured downward from a horizontal reference line—always an acute angle in standard right-triangle applications.
Why It Matters
It is essential for calculating the distance to objects viewed from a height (e.g., from a cliff, aircraft, or tower). In aviation and search-and-rescue, it is the primary metric for locating ground targets from the air.
Core Concepts
- Horizontal Reference: Both the angle of elevation and depression must be measured from a horizontal line. A common pitfall is measuring from the vertical line of a structure.
- Symmetry with Elevation: The angle of depression from point looking down at point is congruent to the Angle of Elevation from point looking up at point . This is because horizontal rays at different altitudes are parallel, making the two angles alternate interior angles.
- Geometry of Sight: The angle of depression provides one of the interior acute angles for the right triangles used in solving height and distance problems.