1. What is Shadow Length Calculation?

Shadow length calculation determines the length of a shadow cast by an object based on its height and the sun's altitude angle. This is a fundamental concept in trigonometry and has practical applications in architecture, photography, and astronomy.

2. How Does the Calculator Work?

The calculator uses the shadow length formula:

Where:

• \( \text{Height} \) — Height of the object in meters
• \( \text{Sun Altitude} \) — Angle of the sun above the horizon in degrees
• \( \tan \) — Trigonometric tangent function

Explanation: The formula uses basic trigonometric principles where the tangent of the sun's altitude angle equals the ratio of the object's height to its shadow length.

3. Importance of Shadow Length Calculation

Details: Calculating shadow length is important for architectural planning to avoid unwanted shadows, in photography for lighting planning, and in various scientific applications including solar energy system design.

4. Using the Calculator

Tips: Enter the object height in meters and the sun altitude angle in degrees (0-90°). Both values must be positive numbers, with sun altitude between 0 and 90 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is sun altitude angle?
A: Sun altitude is the angle between the horizon and the center of the sun's disc, measured in degrees. It ranges from 0° at sunrise/sunset to 90° when the sun is directly overhead.

Q2: Why does the formula use tangent function?
A: In a right triangle formed by the object, its shadow, and the sun's rays, the tangent of the sun angle equals the ratio of opposite side (object height) to adjacent side (shadow length).

Q3: What are typical shadow lengths?
A: Shadow length varies greatly throughout the day. At noon with high sun altitude, shadows are short. During morning/evening with low sun altitude, shadows become much longer.

Q4: Does this work for artificial light sources?
A: Yes, the same principle applies to any light source where the light rays are parallel, such as distant artificial lights.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for point light sources and parallel light rays. For the sun, it provides excellent approximation for most practical purposes.