1. What is the Height Of Pentagon Given Circumradius Using Interior Angle Formula?

The Height Of Pentagon Given Circumradius Using Interior Angle formula calculates the height of a regular pentagon from its circumradius using trigonometric relationships based on the interior angles of the pentagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of Pentagon (m)
• \( r_c \) — Circumradius of Pentagon (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \cos \) — Cosine trigonometric function

Explanation: The formula uses the cosine of three-fifths of π radians (108 degrees), which is derived from the interior angle of a regular pentagon.

3. Importance of Height Calculation

Details: Calculating the height of a pentagon is important in geometry, architecture, and various engineering applications where pentagonal shapes are used.

4. Using the Calculator

Tips: Enter the circumradius of the pentagon in meters. The value must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular pentagon?
A: A regular pentagon is a five-sided polygon where all sides are equal in length and all interior angles are equal (108 degrees each).

Q2: What is the circumradius of a pentagon?
A: The circumradius is the radius of a circle that passes through all the vertices of the pentagon.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact for a regular pentagon, using the precise value of π and cosine function.

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

Q5: What are practical applications of this calculation?
A: This calculation is useful in architectural design, construction, and any field dealing with geometric shapes and measurements.