1. What is Arc Length Approximation?

Arc length approximation using Pythagoras estimates the length of a circular arc by treating it as the hypotenuse of a right triangle formed by the chord and the radial difference.

2. How Does the Calculator Work?

The calculator uses the Pythagorean approximation:

Where:

• \( L \) — Approximate arc length
• \( r \) — Radius of the circle
• \( \theta \) — Central angle in radians

Explanation: This method approximates the curved arc as a straight line (chord) and calculates its length using the Pythagorean theorem.

3. Applications of Arc Length Calculation

Details: Arc length calculations are essential in engineering, architecture, computer graphics, and any field dealing with circular measurements and curved surfaces.

4. Using the Calculator

Tips: Enter the radius and angle values. The angle should be in degrees (0-360). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is this approximation?
A: The approximation is most accurate for small angles. For larger angles, the error increases as the chord deviates more from the actual arc.

Q2: What's the exact formula for arc length?
A: The exact formula is \( L = r \times \theta \) where θ is in radians. Our calculator converts degrees to radians internally.

Q3: When should I use this approximation vs. the exact formula?
A: This approximation is useful for quick calculations and educational purposes. For precise work, use the exact formula \( L = r \times \theta \).

Q4: Can this be used for any circle sector?
A: Yes, this approximation works for any circular arc, regardless of the angle size, though accuracy decreases with larger angles.

Q5: What are the limitations of this method?
A: The main limitation is decreasing accuracy with increasing angle size. For angles approaching 180°, the error becomes significant.