Height of Hendecagon given Diagonal across Five Sides Calculator

Formula Used:

\[ Height = \frac{\left(\frac{Diagonal\ across\ Five\ Sides \times \sin(\pi/11)}{\sin(5\pi/11)}\right)}{2 \times \tan(\pi/22)} \]

Height of Hendecagon:

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1. What is Height of Hendecagon?

The height of a hendecagon is the length of a perpendicular line drawn from one vertex to the opposite side. It represents the maximum vertical distance between parallel sides of the regular hendecagon.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ Height = \frac{\left(\frac{Diagonal\ across\ Five\ Sides \times \sin(\pi/11)}{\sin(5\pi/11)}\right)}{2 \times \tan(\pi/22)} \]

This formula calculates the height of a regular hendecagon based on the diagonal measurement across five of its sides.

3. Formula Explanation

Mathematical Components:

\(\pi\) - Mathematical constant (approximately 3.14159)
\(\sin\) - Sine trigonometric function
\(\tan\) - Tangent trigonometric function
Diagonal across Five Sides - Measurement input by user

The formula utilizes trigonometric relationships specific to the 11-sided polygon geometry to derive the height from the given diagonal measurement.

4. Using the Calculator

Instructions: Enter the diagonal measurement across five sides of the hendecagon in meters. The value must be a positive number. Click "Calculate" to get the height result.

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is an 11-sided polygon. When regular, all sides and angles are equal.

Q2: Why use trigonometric functions in this calculation?
A: Trigonometric functions help relate the diagonal measurement to the height through the internal angles of the regular polygon.

Q3: What units should I use for the diagonal measurement?
A: The calculator uses meters, but you can use any consistent unit as the result will be in the same unit.

Q4: Can this calculator be used for irregular hendecagons?
A: No, this formula only works for regular hendecagons where all sides and angles are equal.

Q5: How accurate is the calculation?
A: The calculation uses precise mathematical constants and functions, providing accurate results based on the input value.