1. What is Diagonal across Three Sides of Nonagon?

Diagonal across Three Sides of Nonagon is the straight line joining two non-adjacent vertices which is across three sides of the Nonagon. It's an important geometric measurement in nonagon (9-sided polygon) analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \pi \) — Archimedes' constant (≈3.14159)
• \( \sin \) — Sine trigonometric function
• \( \cos \) — Cosine trigonometric function
• Inradius of Nonagon — Radius of the circle inscribed inside the Nonagon

3. Formula Explanation

Mathematical Basis: The formula derives from trigonometric relationships in a regular nonagon. The inradius connects to various diagonals through specific angle relationships (3π/9 and π/9) that correspond to the geometric properties of a 9-sided polygon.

4. Using the Calculator

Instructions: Enter the inradius value in meters. The inradius must be a positive number. The calculator will compute the diagonal length across three sides of the nonagon.

5. Frequently Asked Questions (FAQ)

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

Q2: What is the inradius of a polygon?
A: The inradius is the radius of the inscribed circle that touches all sides of the polygon from inside.

Q3: How many diagonals does a nonagon have?
A: A nonagon has 27 diagonals in total, with different lengths depending on how many sides they cross.

Q4: What are the practical applications of this calculation?
A: This calculation is used in geometry, architecture, engineering design, and various fields requiring precise geometric measurements of nonagonal shapes.

Q5: Can this formula be used for irregular nonagons?
A: No, this formula applies only to regular nonagons where all sides and angles are equal. Irregular nonagons require different calculation methods.