1. What is the Breadth of Rectangle Formula?

This calculator computes the breadth of a rectangle using the perimeter and the obtuse angle between its diagonals. The formula provides an alternative method to calculate rectangle dimensions using geometric properties.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( b \) — Breadth of Rectangle (m)
• \( P \) — Perimeter of Rectangle (m)
• \( \angle_{d(obtuse)} \) — Obtuse Angle between Diagonals (°)

Explanation: The formula derives from the trigonometric relationships between rectangle dimensions, perimeter, and the angles formed by its diagonals.

3. Importance of Rectangle Breadth Calculation

Details: Calculating rectangle breadth using diagonal angles is useful in geometric analysis, construction planning, and various engineering applications where diagonal measurements are more accessible than direct side measurements.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why use this method instead of direct measurement?
A: This method is useful when diagonal measurements are available but direct side measurements are difficult to obtain.

Q2: What is the range of valid angle inputs?
A: The obtuse angle must be between 90° and 180° (exclusive of 90°, inclusive of 180°).

Q3: Can this formula be used for squares?
A: Yes, but for squares the diagonals form right angles (90°), so this specific formula for obtuse angles wouldn't apply.

Q4: What units should be used for inputs?
A: Perimeter should be in meters, angle in degrees. The result will be in meters.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, but practical accuracy depends on the precision of input measurements.