Angles of Elevation and Depression

Angle of Elevation

The Angle formed from the horizontal upward to a Line of sight. You look UP from your position to an object above.

Angle of Depression

The Angle formed from the horizontal downward to a Line of sight. You look DOWN from your position to an object below.

Key Relationship

The Angle of elevation from Point A to Point B equals the Angle of depression from Point B to Point A (alternate interior angles).

Solving Problems

1. Draw a diagram with a right Triangle.
2. Identify the Angle (elevation or depression).
3. Label the known and unknown sides.
4. Choose the trig ratio (sin, cos, or tan) that connects the known and unknown.
5. Solve.

Example: A person standing 50 m from a building looks up at the top with an Angle of elevation of 60°. Height = 50 × tan 60° = 50√3 ≈ 86.6 m.