Diagonal Of Hendecagon Across Three Sides Given Height Calculator

Formula Used:

\[ Diagonal\ across\ Three\ Sides\ of\ Hendecagon = \frac{2 \times \tan(\pi/22) \times Height \times \sin((3\pi)/11)}{\sin(\pi/11)} \]

Diagonal across Three Sides of Hendecagon:

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1. What is Diagonal across Three Sides of Hendecagon?

Diagonal across Three Sides of Hendecagon is a straight line joining two non-adjacent sides across three sides of the Hendecagon. It's an important geometric measurement in an 11-sided polygon.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ d_3 = \frac{2 \times \tan(\pi/22) \times h \times \sin((3\pi)/11)}{\sin(\pi/11)} \]

Where:

\( d_3 \) — Diagonal across three sides of Hendecagon
\( h \) — Height of Hendecagon (m)
\( \pi \) — Mathematical constant pi (≈3.14159)

3. Formula Explanation

Details: This formula derives from trigonometric relationships within a regular Hendecagon (11-sided polygon). The tangent and sine functions help establish the proportional relationship between the height and the diagonal measurement across three sides.

4. Using the Calculator

Tips: Enter the height of the Hendecagon in meters. The height must be a positive value greater than zero. The calculator will compute the diagonal measurement across three sides.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hendecagon?
A: A Hendecagon is an 11-sided polygon, also known as an undecagon. It's a regular polygon where all sides and angles are equal.

Q2: Why use trigonometric functions in this calculation?
A: Trigonometric functions help establish precise geometric relationships between different measurements in regular polygons, allowing accurate calculations of diagonals and other properties.

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

Q4: What are practical applications of this calculation?
A: This calculation is useful in geometry, architecture, engineering design, and any field dealing with polygonal structures and their measurements.

Q5: How accurate is the calculation?
A: The calculation uses precise mathematical constants and functions, providing highly accurate results when correct input values are provided.