1. What is a Circumdiameter Calculator?

Definition: This calculator computes the diameter of a triangle's circumscribed circle (circumcircle) based on one side length and its opposite angle.

Purpose: It helps in geometry problems and construction projects where triangular dimensions are involved.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( D \) — Diameter of the circumcircle (meters)
• \( a \) — Length of one side of the triangle (meters)
• \( A \) — Angle opposite to side a (degrees)

Explanation: The side length is divided by the sine of its opposite angle to determine the diameter of the circumscribed circle.

3. Importance of Circumdiameter Calculation

Details: Knowing the circumdiameter is essential for geometric constructions, determining the smallest enclosing circle for a triangle, and various engineering applications.

4. Using the Calculator

Tips: Enter the side length in meters and the opposite angle in degrees (must be between 0 and 180). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a circumcircle?
A: A circumcircle is a circle that passes through all three vertices of a triangle.

Q2: Does this work for any type of triangle?
A: Yes, the formula works for acute, right, and obtuse triangles.

Q3: What if I know two sides and an included angle?
A: You would need to first calculate the opposite side using the Law of Cosines before using this calculator.

Q4: Why does the angle need to be less than 180°?
A: In Euclidean geometry, a triangle's angles must sum to 180°, so no single angle can be 180° or more.

Q5: Can I use this for other polygons?
A: No, this formula is specific to triangles. Other polygons have different circumradius formulas.