1. What Is The Chord Length Of Circle Given Diameter And Inscribed Angle Formula?

The chord length of a circle given diameter and inscribed angle formula calculates the length of a chord in a circle using the circle's diameter and an inscribed angle. This formula is derived from trigonometric relationships in circle geometry.

2. How Does The Calculator Work?

The calculator uses the formula:

Where:

• \( l_c \) — Chord Length of Circle (m)
• \( D \) — Diameter of Circle (m)
• \( \angle_{\text{Inscribed}} \) — Inscribed Angle of Circle (rad)

Explanation: The formula uses the sine trigonometric function to relate the chord length to the diameter and inscribed angle of the circle.

3. Importance Of Chord Length Calculation

Details: Calculating chord lengths is essential in various geometric applications, including engineering design, architectural planning, and mathematical problem-solving involving circular segments.

4. Using The Calculator

Tips: Enter the diameter in meters and the inscribed angle in radians. Both values must be positive numbers (diameter > 0, angle ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is a chord in a circle?
A: A chord is a straight line segment whose endpoints lie on the circumference of the circle.

Q2: How does the inscribed angle affect the chord length?
A: The chord length increases as the sine of the inscribed angle increases, reaching maximum when the angle is π/2 radians (90 degrees).

Q3: Can this formula be used for any inscribed angle?
A: Yes, the formula works for any inscribed angle between 0 and π radians (0-180 degrees).

Q4: What are the units for the inputs and outputs?
A: The calculator uses meters for length measurements and radians for angle measurements.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the trigonometric relationship, assuming accurate input values.