Breadth of Rectangle Given Diameter of Circumcircle and Angle between Diagonal and Length Calculator

Formula Used:

\[ b = D_c \times \sin(\angle dl) \]

Breadth of Rectangle:

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1. What is the Breadth of Rectangle Formula?

The formula calculates the breadth of a rectangle using the diameter of its circumcircle and the angle between the diagonal and the length. This relationship is derived from trigonometric properties of rectangles and circles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = D_c \times \sin(\angle dl) \]

Where:

\( b \) — Breadth of Rectangle (m)
\( D_c \) — Diameter of Circumcircle of Rectangle (m)
\( \angle dl \) — Angle between Diagonal and Length of Rectangle (°)

Explanation: The formula uses the sine trigonometric function to relate the angle between the diagonal and length with the breadth of the rectangle through the circumcircle diameter.

3. Importance of Rectangle Breadth Calculation

Details: Calculating the breadth of a rectangle is essential in geometry, architecture, engineering, and various design applications where precise dimensions are required.

4. Using the Calculator

Tips: Enter the diameter of the circumcircle in meters and the angle in degrees between 0 and 90. All values must be valid 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 a 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 angle between the diagonal and length to the ratio of the opposite side (breadth) to the hypotenuse (diagonal/diameter).

Q3: What are the valid angle values?
A: The angle between the diagonal and length must be between 0° and 90°. At 0°, the breadth would be 0, and at 90°, the breadth equals the diameter.

Q4: Can this formula be used for squares?
A: Yes, for a square, the angle between the diagonal and any side is 45°, and the formula will correctly calculate the side length.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the inputs. Accuracy depends on the precision of the measurements provided.