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Height Calculation Formula:
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Shadow casting height calculation uses trigonometry to determine the height of an object based on the length of its shadow and the angle of the sun. This method is commonly used in surveying, architecture, and outdoor measurements.
The calculator uses the trigonometric formula:
Where:
Explanation: The tangent of the sun angle represents the ratio of the object's height to its shadow length, allowing us to calculate height when shadow length and angle are known.
Details: This calculation method is valuable for estimating heights of inaccessible objects like buildings, trees, or mountains without direct measurement tools.
Tips: Enter shadow length in meters and sun angle in degrees (between 0-90). Ensure measurements are accurate for precise results. The sun angle should be measured at the same time the shadow is measured.
Q1: What is the optimal time for shadow measurements?
A: Mid-morning or mid-afternoon when shadows are distinct and sun angle is between 30-60 degrees provides the most accurate results.
Q2: How accurate is this method?
A: Accuracy depends on precise measurement of both shadow length and sun angle. With careful measurement, results can be within 2-5% of actual height.
Q3: Can this be used for very tall objects?
A: Yes, but for very tall objects, atmospheric refraction may affect accuracy, and the calculation assumes the ground is level.
Q4: What tools are needed to measure sun angle?
A: A clinometer, sextant, or smartphone app with angle measurement capability can be used to measure the sun's angle.
Q5: Are there limitations to this method?
A: The method assumes the object is vertical, the ground is level, and the shadow endpoint is clearly visible. Results may be less accurate on uneven terrain or with objects that aren't perfectly vertical.