Side of Hendecagon given Diagonal across Two Sides Calculator

Formula Used:

\[ S = \frac{d_2 \times \sin(\pi/11)}{\sin(2\pi/11)} \]

Side of Hendecagon:

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1. What is the Side of Hendecagon given Diagonal across Two Sides Formula?

The formula calculates the side length of a regular hendecagon (11-sided polygon) when the diagonal across two sides is known. It uses trigonometric relationships specific to the geometry of an 11-sided polygon.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ S = \frac{d_2 \times \sin(\pi/11)}{\sin(2\pi/11)} \]

Where:

\( S \) — Side of Hendecagon (m)
\( d_2 \) — Diagonal across Two Sides of Hendecagon (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \sin \) — Sine trigonometric function

Explanation: The formula utilizes the trigonometric properties of a regular hendecagon, where the angles between sides and diagonals follow specific patterns based on the polygon's symmetry.

3. Importance of Hendecagon Side Calculation

Details: Calculating the side length of a hendecagon is important in geometric design, architectural planning, and mathematical applications involving regular polygons. It helps in determining the precise dimensions of 11-sided structures.

4. Using the Calculator

Tips: Enter the diagonal across two sides in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular hendecagon?
A: A regular hendecagon is an 11-sided polygon where all sides are equal in length and all internal angles are equal (approximately 147.27 degrees each).

Q2: Why are trigonometric functions used in this calculation?
A: Trigonometric functions help establish the relationship between the diagonal and side length through the angles formed in the regular polygon's geometry.

Q3: Can this formula be used for irregular hendecagons?
A: No, this formula is specifically designed for regular hendecagons where all sides and angles are equal.

Q4: What are practical applications of hendecagon calculations?
A: Hendecagons are used in architectural design, coin design (such as the Canadian dollar coin), and various mathematical and geometric studies.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular hendecagons, with accuracy depending on the precision of the input value and the trigonometric function implementations.