1. What Is Major Arc Length?

The Major Arc Length of a Circular Arc is the length of the largest arc cut from a circle using any two arbitrary points on the circle. It represents the longer path between two points on a circle's circumference.

2. How Does The Calculator Work?

The calculator uses the formula:

Where:

• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( Tangent\ Angle \) — Angle subtended by tangents at endpoints (radians)
• \( Radius \) — Radius of the circular arc (meters)

Explanation: This formula calculates the length of the major arc by combining the constant π with the tangent angle, then multiplying by the radius of the circle.

3. Importance Of Major Arc Length Calculation

Details: Calculating major arc length is essential in geometry, engineering, and architecture for designing curved structures, calculating distances along circular paths, and solving problems involving circular motion.

4. Using The Calculator

Tips: Enter the tangent angle in radians and the radius in meters. Both values must be positive numbers. The calculator will compute the major arc length of the circular arc.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between major and minor arc length?
A: The major arc is the longer path between two points on a circle, while the minor arc is the shorter path. Together they complete the full circumference.

Q2: Can I use degrees instead of radians?
A: The formula requires radians. Convert degrees to radians by multiplying by π/180 before calculation.

Q3: What is the relationship between tangent angle and central angle?
A: The tangent angle is supplementary to the central angle subtended by the same chord.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact when using precise values for π and the tangent angle.

Q5: Can this formula be used for any circular arc?
A: Yes, this formula applies to any circular arc where you know the radius and tangent angle.