1. What is the Shadow Length Formula?

The shadow length formula calculates the length of a shadow cast by an object based on the object's height and the angle of the light source. This trigonometric relationship is fundamental in geometry and has practical applications in various fields.

2. How Does the Calculator Work?

The calculator uses the shadow length formula:

Where:

• Object Height — Height of the object in meters
• Angle of Light — Angle of the light source in degrees (0-90)

Explanation: The formula uses the tangent trigonometric function to calculate the ratio between the object's height and its shadow length based on the light angle.

3. Importance of Shadow Length Calculation

Details: Shadow length calculations are important in architecture, photography, astronomy, and various engineering fields where light and shadow relationships need to be precisely determined.

4. Using the Calculator

Tips: Enter object height in meters and light angle in degrees (between 0 and 90). Both values must be positive numbers, with the angle less than 90 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What happens when the light angle is 90 degrees?
A: At 90 degrees (directly overhead), the shadow length approaches zero as the tangent of 90 degrees approaches infinity.

Q2: Can this formula be used for any light source?
A: Yes, the formula works for any directional light source where the light rays are parallel, such as sunlight.

Q3: What units should be used for the measurements?
A: The calculator uses meters for height, but any consistent length unit can be used as long as both input and output use the same unit.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise for point light sources or parallel light rays. For extended light sources, the shadow may have some penumbra effects.

Q5: Can this be used for inclined surfaces?
A: The basic formula assumes a flat, horizontal surface. For inclined surfaces, additional trigonometric calculations would be needed.