1. What is the Edge Length of Equilateral Triangle given Exradius?

The edge length of an equilateral triangle can be calculated from its exradius using the mathematical relationship between these two geometric properties. The exradius is the radius of the excircle tangent to one side of the triangle and the extensions of the other two sides.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Equilateral Triangle (m)
• \( r_e \) — Exradius of Equilateral Triangle (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula derives from the geometric relationship between the side length and exradius in an equilateral triangle, where the exradius is related to the side length through trigonometric relationships.

3. Importance of Edge Length Calculation

Details: Calculating the edge length from the exradius is important in geometry problems, architectural design, and engineering applications where equilateral triangles are used. It helps in determining the size and proportions of triangular structures and components.

4. Using the Calculator

Tips: Enter the exradius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding edge length of the equilateral triangle.

5. Frequently Asked Questions (FAQ)

Q1: What is an exradius in an equilateral triangle?
A: The exradius is the radius of an excircle, which is a circle tangent to one side of the triangle and the extensions of the other two sides.

Q2: How is this formula derived?
A: The formula is derived from the geometric properties of equilateral triangles and the relationship between side length, exradius, and the angles of the triangle.

Q3: Can this formula be used for other types of triangles?
A: No, this specific formula applies only to equilateral triangles where all sides and angles are equal.

Q4: What are practical applications of this calculation?
A: This calculation is useful in engineering, architecture, and design where equilateral triangular components are used, such as in truss structures, decorative elements, and mechanical parts.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles. The accuracy depends on the precision of the input exradius value.