Diameter Of Circumcircle Of Rectangle Given Breadth And Angle Between Diagonal And Breadth Calculator

Formula Used:

\[ D_c = b \times \csc\left(\frac{\pi}{2} - \angle_{db}\right) \]

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 diameter is equal to the length of the diagonal of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D_c = b \times \csc\left(\frac{\pi}{2} - \angle_{db}\right) \]

Where:

\( D_c \) — Diameter of circumcircle (m)
\( b \) — Breadth of rectangle (m)
\( \angle_{db} \) — Angle between diagonal and breadth (degrees)
\( \csc \) — Cosecant trigonometric function
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula calculates the diameter of the circumcircle using the breadth of the rectangle and the angle between the diagonal and the breadth.

3. Importance of Circumcircle Diameter Calculation

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

4. Using the Calculator

Tips: Enter the breadth of the rectangle in meters and the angle between the diagonal and breadth in degrees. The angle must be between 0 and 90 degrees, and the breadth must be a positive value.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between the circumcircle diameter and the rectangle's diagonal?
A: The diameter of the circumcircle is exactly equal to the length of the rectangle's diagonal.

Q2: Can this formula be used for squares?
A: Yes, since a square is a special case of a rectangle, this formula applies to squares as well.

Q3: What is the range of valid angle values?
A: The angle between the diagonal and breadth must be between 0 and 90 degrees (exclusive).

Q4: How is the cosecant function related to this calculation?
A: The cosecant function (csc) is the reciprocal of the sine function, and it helps relate the breadth to the diagonal through the given angle.

Q5: What are practical applications of this calculation?
A: This calculation is useful in various fields including architecture, mechanical engineering, computer graphics, and any application where rectangular objects need to be inscribed within circular boundaries.