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Diagonal Of Decagon Across Two Sides Given Diagonal Across Three Sides Calculator

Formula Used:

\[ Diagonal\ Across\ Two\ Sides\ of\ Decagon = \frac{\sqrt{10+(2\times\sqrt{5})}}{2} \times \frac{2 \times Diagonal\ Across\ Three\ Sides\ of\ Decagon}{\sqrt{14+(6\times\sqrt{5})}} \]

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1. What is the Diagonal Across Two Sides of Decagon?

The Diagonal Across Two Sides of a Decagon is a straight line joining two non-adjacent vertices that are separated by two sides. In a regular decagon, all diagonals have specific mathematical relationships based on the golden ratio and trigonometric properties.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ d2 = \frac{\sqrt{10+(2\times\sqrt{5})}}{2} \times \frac{2 \times d3}{\sqrt{14+(6\times\sqrt{5})}} \]

Where:

Explanation: This formula establishes the precise mathematical relationship between the diagonal across two sides and the diagonal across three sides in a regular decagon, utilizing properties of the golden ratio and trigonometric identities.

3. Geometric Properties of Decagon

Details: A regular decagon has 10 equal sides and 10 equal angles. The diagonals in a decagon follow specific patterns and ratios that are derived from the geometry of regular polygons and the mathematical constant φ (phi), also known as the golden ratio.

4. Using the Calculator

Tips: Enter the length of the diagonal across three sides of the decagon in meters. The value must be positive and greater than zero. The calculator will compute the corresponding diagonal across two sides.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular decagon?
A: A regular decagon is a polygon with 10 equal sides and 10 equal interior angles of 144 degrees each.

Q2: How many diagonals does a decagon have?
A: A decagon has 35 diagonals in total, with different lengths depending on how many sides they span.

Q3: What is the relationship between different diagonals?
A: The diagonals in a regular decagon follow specific mathematical relationships based on the golden ratio (approximately 1.618).

Q4: Can this calculator be used for irregular decagons?
A: No, this calculator is specifically designed for regular decagons where all sides and angles are equal.

Q5: What are practical applications of this calculation?
A: This calculation is useful in geometry, architecture, design, and any field dealing with regular polygonal structures.

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