Trigonometry in Action
Measuring Heights Using Clinometers
Explore how trigonometry can be used to measure heights of objects using angle measurements from a clinometer. Adjust the angle to see how it affects the calculated height!
Calculated Height: 34.64m
Distance: 20m
Angle: 60°
Observation:
At 60° angle and 20m distance, the height is calculated as 20 × tan(60°) = 34.64m.
The Mathematics Behind Height Measurement
Key Concepts:
Trigonometry allows us to calculate heights using angle measurements and known distances:
- Tangent function: tan(θ) = opposite/adjacent
- Height calculation: height = distance × tan(angle)
- Clinometer: Device to measure angles of elevation
Practical Applications:
This method is used by surveyors, foresters, and engineers to measure heights of trees, buildings, and other tall objects without direct measurement.
Calculation Steps:
- Measure the distance from the observer to the object (adjacent side)
- Measure the angle of elevation to the top of the object
- Calculate height using tangent function: height = distance × tan(angle)
- Add the observer's eye height for total object height
