Height of Object using Angle of Elevation

\[h=d\tan(\theta)\]

h = height of the object (m)

d = horizontal distance to the object (m)

theta = angle of elevation (rad or °)

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

The angle of elevation is measured upward from the horizontal line of sight to the top of the object.

The tangent function relates the opposite side of a right triangle to its adjacent side.

Use this formula when:

- The horizontal distance to the object is known

- The angle of elevation is measured

- Direct height measurement is difficult or impossible

- Solving surveying or construction problems

- Working with observation and distance calculations

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

If:

d = 40 m

theta = 30°

Then:

h = 40*tan(30°)

h ≈ 23.09 m

- Surveying and mapping

- Construction and engineering

- Architecture

- Navigation and observation systems

- Physics and mechanics

- Educational trigonometry

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