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

Formula Used:

\[ P = 2 \times D_c \times \sqrt{1 + (2 \times \sin((\pi/2) - \angle_{db}) \times \cos((\pi/2) - \angle_{db}))} \]

Perimeter of Rectangle (P):

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1. What is the Perimeter of Rectangle given Diameter of Circumcircle and Angle between Diagonal and Breadth?

This calculation determines the perimeter of a rectangle when you know the diameter of its circumcircle and the angle between the diagonal and the breadth of the rectangle. The circumcircle is the circle that passes through all four vertices of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P = 2 \times D_c \times \sqrt{1 + (2 \times \sin((\pi/2) - \angle_{db}) \times \cos((\pi/2) - \angle_{db}))} \]

Where:

\( P \) — Perimeter of Rectangle (m)
\( D_c \) — Diameter of Circumcircle of Rectangle (m)
\( \angle_{db} \) — Angle between Diagonal and Breadth of Rectangle (rad)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula uses trigonometric functions (sine and cosine) and square root to calculate the perimeter based on the given geometric properties of the rectangle.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a rectangle is fundamental in geometry and has practical applications in construction, design, and various engineering fields where rectangular shapes are involved.

4. Using the Calculator

Tips: Enter the diameter of the circumcircle in meters and the angle between the diagonal and breadth in radians. The angle should be between 0 and π/2 radians (0-90 degrees).

5. Frequently Asked Questions (FAQ)

Q1: What is a circumcircle of a rectangle?
A: A circumcircle is a circle that passes through all the vertices of a polygon. For a rectangle, the circumcircle's center is at the intersection of the diagonals.

Q2: Why is the angle measured in radians?
A: Radians are the standard unit for angle measurement in mathematical calculations, particularly when using trigonometric functions.

Q3: Can I use degrees instead of radians?
A: The calculator requires input in radians. To convert degrees to radians, multiply by π/180.

Q4: What is the relationship between the diameter and the rectangle's diagonal?
A: For a rectangle, the diameter of the circumcircle is equal to the length of the diagonal of the rectangle.

Q5: Are there any limitations to this formula?
A: This formula specifically applies to rectangles and requires accurate measurement of the diameter and angle for precise results.