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The formula calculates the side length of a regular nonagon (9-sided polygon) when the circumradius (distance from center to vertex) is known. This geometric relationship is derived from trigonometric principles applied to regular polygons.
The calculator uses the formula:
Where:
Explanation: The formula uses the sine function to calculate the side length based on the central angle of the nonagon (40° or π/9 radians) and the given circumradius.
Details: Calculating the side length of a regular nonagon is essential in geometry, architecture, and engineering applications where nonagonal shapes are used. It helps in determining perimeter, area, and other geometric properties.
Tips: Enter the circumradius value in meters. The value must be positive and greater than zero for accurate calculation.
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 is the formula derived?
A: The formula is derived from the trigonometric relationship in a right triangle formed by the circumradius, half the side length, and the central angle (360°/9 = 40°).
Q3: What are practical applications of this calculation?
A: This calculation is used in architectural design, mechanical engineering, and geometric pattern creation where nonagonal shapes are employed.
Q4: Can this formula be used for irregular nonagons?
A: No, this formula applies only to regular nonagons where all sides and angles are equal.
Q5: What is the relationship between side length and circumradius?
A: The side length is directly proportional to the circumradius, with the constant of proportionality being 2×sin(π/9) ≈ 0.68404.