1. What is the Sun Height Equation?

The Sun Height equation calculates the height of an object (like the sun) based on the length of its shadow and the angle of elevation. This trigonometric relationship is fundamental in astronomy, architecture, and surveying.

2. How Does the Calculator Work?

The calculator uses the trigonometric equation:

Where:

• \( Shadow \) — Length of the shadow in meters
• \( Angle \) — Angle of elevation in degrees (0-90)
• \( \tan \) — Tangent trigonometric function

Explanation: The tangent of the angle equals the ratio of the opposite side (height) to the adjacent side (shadow length) in a right triangle.

3. Importance of Sun Angle Measurement

Details: Measuring sun height and angles is crucial for solar panel positioning, architectural design, photography, and understanding seasonal changes in sunlight.

4. Using the Calculator

Tips: Enter shadow length in meters and sun angle in degrees (must be between 0 and 90). For best results, measure the shadow at solar noon when the sun is at its highest point.

5. Frequently Asked Questions (FAQ)

Q1: What's the most accurate time to measure shadows?
A: Solar noon (when the sun is highest in the sky) provides the most consistent measurements as shadows are shortest and direction is most consistent.

Q2: Can this be used for any object?
A: Yes, the equation works for any object where you can measure both the shadow length and the angle of elevation to the top.

Q3: Why does the angle need to be less than 90 degrees?
A: At 90 degrees, the sun would be directly overhead with no shadow (tan(90) is undefined). Practical angles are always less than 90.

Q4: How accurate is this method?
A: Accuracy depends on precise measurement of both shadow length and angle. Small errors in angle measurement can significantly affect results.

Q5: Can I use this to calculate shadow length if I know the height?
A: Yes, the equation can be rearranged: \( Shadow = Height / \tan(Angle) \).