Breadth of Rectangle given Diameter of Circumcircle and Acute Angle between Diagonals Calculator

Formula Used:

\[ b = D_c \times \sin\left(\frac{\angle d_{Acute}}{2}\right) \]

Breadth of Rectangle (b):

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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 acute angle between its diagonals. This geometric relationship helps determine one dimension of a rectangle when certain properties are known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = D_c \times \sin\left(\frac{\angle d_{Acute}}{2}\right) \]

Where:

\( b \) — Breadth of Rectangle (m)
\( D_c \) — Diameter of Circumcircle of Rectangle (m)
\( \angle d_{Acute} \) — Acute Angle between Diagonals of Rectangle (°)

Explanation: The formula derives from trigonometric relationships in a rectangle and its circumscribed circle, where the breadth can be expressed in terms of the circumcircle diameter and the angle between diagonals.

3. Importance of Rectangle Breadth Calculation

Details: Calculating the breadth of a rectangle is essential in various geometric applications, construction projects, and engineering designs where precise dimensions are required.

4. Using the Calculator

Tips: Enter the diameter of the circumcircle in meters and the acute angle between diagonals in degrees. Both values must be positive, with the angle between 0° and 90°.

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 any rectangle, the circumcircle's center is at the intersection of the diagonals.

Q2: Why is the angle divided by 2 in the formula?
A: The division by 2 comes from the trigonometric identity and the geometric relationship between the rectangle's dimensions and the angles formed by its diagonals.

Q3: Can this formula be used for squares?
A: Yes, since a square is a special type of rectangle, this formula applies to squares as well, where the acute angle between diagonals is 90°.

Q4: What are the units of measurement?
A: The calculator uses meters for length measurements and degrees for angles. Ensure consistent units for accurate results.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of rectangles. Accuracy depends on the precision of input values.