1. What is the Side of Nonagon Given Diagonal Across Three Sides Formula?

The formula calculates the side length of a regular nonagon (9-sided polygon) when the diagonal across three sides is known. This geometric relationship is derived from trigonometric principles applied to regular polygons.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( S \) — Side length of the nonagon
• \( d_3 \) — Diagonal across three sides of the nonagon
• \( \pi \) — Mathematical constant (approximately 3.14159)
• \( \sin \) — Sine trigonometric function

Explanation: The formula utilizes the trigonometric relationships between the angles in a regular nonagon to establish the proportion between the side length and the diagonal spanning three sides.

3. Importance of Side Length Calculation

Details: Calculating the side length from a known diagonal is essential in geometric design, architectural planning, and various engineering applications where regular nonagonal shapes are used.

4. Using the Calculator

Tips: Enter the diagonal across three sides in meters. The value must be positive and greater than zero. The calculator will compute the corresponding side length of the regular nonagon.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular nonagon?
A: A regular nonagon is a nine-sided polygon where all sides are equal in length and all interior angles are equal (140° each).

Q2: How many diagonals does a nonagon have?
A: A nonagon has 27 diagonals in total, with different lengths depending on how many sides they span.

Q3: Can this formula be used for irregular nonagons?
A: No, this formula applies only to regular nonagons where all sides and angles are equal.

Q4: What are practical applications of nonagons?
A: Nonagons are used in architecture, design, coin minting (some countries), and various decorative patterns.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular nonagons, though practical measurements may introduce some error.