Distance using Angle of Depression

\[d=\frac{h}{\tan(\theta)}\]

Variables

dhorizontal distance to the object (m)

hvertical height difference (m)

thetaangle of depression (rad or °)

This trigonometric formula calculates the horizontal distance to an object using the angle of depression and the vertical height difference.

The angle of depression is measured downward from a horizontal reference line to the line of sight toward the object.

The tangent function relates the vertical height difference to the horizontal distance in a right triangle.

Use this formula when:

- The vertical height difference is known

- The angle of depression is measured

- The horizontal distance must be determined

- Solving surveying or navigation problems

- Working with elevated observation points

The angle may be expressed in degrees or radians depending on calculator settings.

If:

h = 25 m

theta = 40°

Then:

d = 25/tan(40°)

d ≈ 29.79 m

- Surveying and mapping

- Civil engineering

- Navigation systems

- Observation and monitoring

- Physics calculations

- Educational trigonometry