1. What is the Length of Rectangle Formula?

This calculator computes the length of a rectangle using the diameter of its circumcircle and the angle between the diagonal and the breadth. The formula is derived from trigonometric relationships in rectangular geometry.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l \) — Length of the rectangle (m)
• \( D_c \) — Diameter of the circumcircle (m)
• \( \theta_{db} \) — Angle between diagonal and breadth (°)

Explanation: The formula utilizes the sine trigonometric function to relate the length of the rectangle to the diameter of its circumscribed circle and the specified angle.

3. Geometric Interpretation

Details: In a rectangle inscribed in a circle, the diagonal equals the diameter of the circumcircle. The length can be found using trigonometric ratios based on the angle between the diagonal and the breadth.

4. Using the Calculator

Tips: Enter the diameter of the circumcircle in meters and the angle in degrees (between 0° and 90°). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a circumcircle of a rectangle?
A: A circumcircle is a circle that passes through all four vertices of the rectangle. For a rectangle, the diameter of the circumcircle equals the length of the diagonal.

Q2: Why use the sine function in this formula?
A: The sine function relates the opposite side (length) to the hypotenuse (diagonal/diameter) in the right triangle formed by the diagonal, length, and breadth.

Q3: What angle range is valid for this calculation?
A: The angle between diagonal and breadth must be between 0° and 90° for a valid rectangle configuration.

Q4: Can this formula be used for squares?
A: Yes, for a square (where length = breadth), the angle between diagonal and breadth is 45°, and the formula still applies.

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