1. What is the Breadth of Rectangle Formula?

This calculator computes the breadth of a rectangle using its circumradius and the obtuse angle between its diagonals. The formula provides an alternative method to calculate breadth when these specific parameters are known.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( b \) — Breadth of Rectangle (m)
• \( r_c \) — Circumradius of Rectangle (m)
• \( \angle_{d(Obtuse)} \) — Obtuse Angle between Diagonals of Rectangle (°)

Explanation: The formula derives from trigonometric relationships in a rectangle, where the circumradius connects to the rectangle's geometry through the angle between diagonals.

3. Importance of Breadth Calculation

Details: Calculating breadth using circumradius and diagonal angle is useful in geometric problems, construction, and design where these specific measurements are known or easier to obtain.

4. Using the Calculator

Tips: Enter circumradius in meters, obtuse angle between diagonals in degrees (must be between 90° and 180°). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle required to be obtuse?
A: In a rectangle, the diagonals create both acute and obtuse angles. This formula specifically uses the obtuse angle between the diagonals.

Q2: What is the relationship between circumradius and rectangle dimensions?
A: The circumradius of a rectangle is half the length of its diagonal, connecting the center to any vertex.

Q3: Can this formula be used for squares?
A: Yes, since a square is a special type of rectangle, though the obtuse angle between diagonals in a square is 135°.

Q4: What are typical units for these measurements?
A: While meters are used here, any consistent unit of length can be used for breadth and circumradius.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values, with precision limited only by measurement accuracy and computational rounding.