1. What is Height of Nonagon given Circumradius?

The Height of a Nonagon given its Circumradius is the perpendicular distance from one vertex to the opposite side, calculated based on the radius of the circumscribed circle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of Nonagon (m)
• \( r_c \) — Circumradius of Nonagon (m)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)
• \( \cos \) — Cosine trigonometric function

Explanation: The formula calculates the height of a regular nonagon based on its circumradius using trigonometric relationships.

3. Importance of Height Calculation

Details: Calculating the height of a nonagon is important in geometry, architecture, and engineering for determining the vertical dimension of nonagonal structures and components.

4. Using the Calculator

Tips: Enter the circumradius of the nonagon in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a nonagon?
A: A nonagon is a nine-sided polygon. A regular nonagon has all sides and angles equal.

Q2: How is circumradius different from inradius?
A: Circumradius is the radius of the circle that passes through all vertices, while inradius is the radius of the circle inscribed within the polygon.

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

Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, engineering projects, and geometric analysis involving nonagonal shapes.

Q5: How accurate is this formula?
A: The formula is mathematically exact for regular nonagons and provides precise results when accurate input values are used.