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

Formula Used:

\[ D_c = b \times \csc(\angle_{dl}) \]

Diameter of Circumcircle of Rectangle:

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1. What is the Diameter of Circumcircle of Rectangle?

The diameter of the circumcircle of a rectangle is the diameter of the circle that passes through all four vertices of the rectangle. For any rectangle, the circumcircle's center is at the intersection of the diagonals, and its diameter equals the length of the diagonal of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D_c = b \times \csc(\angle_{dl}) \]

Where:

\( D_c \) — Diameter of circumcircle of rectangle (m)
\( b \) — Breadth of rectangle (m)
\( \angle_{dl} \) — Angle between diagonal and length of rectangle (°)
\( \csc \) — Cosecant trigonometric function

Explanation: This formula derives from the trigonometric relationship between the rectangle's breadth, the angle between the diagonal and length, and the resulting diagonal length which equals the circumcircle diameter.

3. Importance of Circumcircle Diameter Calculation

Details: Calculating the circumcircle diameter is important in geometry, engineering design, and architectural planning where circular elements need to encompass rectangular components or where the relationship between rectangular and circular geometries must be determined.

4. Using the Calculator

Tips: Enter the breadth of the rectangle in meters and the angle between the diagonal and length in degrees. The angle must be between 0° and 90°. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why use the cosecant function in this formula?
A: The cosecant function (csc) is the reciprocal of sine, and it's used here to relate the breadth of the rectangle to the diagonal through the given angle between the diagonal and the length.

Q2: What is the relationship between the diagonal and the circumcircle diameter?
A: For any rectangle, the diagonal of the rectangle equals the diameter of its circumcircle.

Q3: Can this formula be used for squares?
A: Yes, since a square is a special case of rectangle, this formula applies to squares as well.

Q4: What is the range of valid angles for this calculation?
A: The angle between the diagonal and length must be between 0° and 90°, exclusive.

Q5: How is this calculation useful in practical applications?
A: This calculation is useful in various fields including mechanical engineering, architecture, and computer graphics where the relationship between rectangular objects and their circumscribing circles needs to be determined.