1. What is the Side Length Formula?

The side length formula \( a = 2 R \sin A \) calculates the length of a side of a triangle when you know the circumradius (R) and the angle opposite that side (A). This formula is derived from the extended law of sines and works for any triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — Length of the side (same units as R)
• \( R \) — Circumradius of the triangle (distance from center to vertex)
• \( A \) — Angle opposite side a (in degrees)

Explanation: The formula relates the side length to the triangle's circumradius and the angle opposite that side through the sine function.

3. Importance of Side Length Calculation

Details: Calculating side lengths from circumradius and angles is essential in trigonometry, geometry, and various engineering applications where triangle properties need to be determined.

4. Using the Calculator

Tips: Enter the circumradius in any length units, and the angle in degrees. The result will be in the same units as the circumradius. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does this formula work for all triangles?
A: Yes, this formula works for acute, right, and obtuse triangles.

Q2: What if I have the angle in radians?
A: You would need to convert the angle to degrees first, or modify the formula to use the angle directly in radians.

Q3: How accurate is this calculation?
A: The accuracy depends on the precision of your input values and the calculator's floating-point precision.

Q4: Can I use this for right triangles?
A: Yes, for a right triangle, the hypotenuse is equal to twice the circumradius (2R).

Q5: What are practical applications of this formula?
A: This is used in navigation, construction, computer graphics, and any field requiring precise geometric calculations.