Side Of Nonagon Given Inradius Calculator

Formula Used:

\[ S = 2 \times r_i \times \tan(\pi/9) \]

Side of Nonagon:

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1. What is the Side of Nonagon given Inradius Formula?

The formula calculates the side length of a regular nonagon (9-sided polygon) when the inradius (radius of the inscribed circle) is known. This geometric relationship helps in determining the dimensions of a nonagon from its inscribed circle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ S = 2 \times r_i \times \tan(\pi/9) \]

Where:

\( S \) — Side of Nonagon (meters)
\( r_i \) — Inradius of Nonagon (meters)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \tan \) — Tangent trigonometric function

Explanation: The formula derives from the geometric properties of a regular nonagon, where the inradius connects the center to the midpoint of a side, forming a right triangle with half the side length.

3. Importance of Side Calculation

Details: Calculating the side length from the inradius is essential in geometry, architecture, and engineering for designing and constructing nonagonal structures and patterns.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

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

Q2: How is the inradius related to the side length?
A: The inradius is perpendicular to the midpoint of a side, forming a right triangle where the tangent of half the central angle relates the inradius to half the side length.

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 this calculation?
A: This calculation is used in architectural design, engineering projects, and geometric pattern creation involving nonagonal shapes.

Q5: How accurate is the trigonometric calculation?
A: The calculation is mathematically exact for a regular nonagon, though practical measurements may have slight variations due to rounding.