1. What is the Breadth of Rectangle Formula?

The formula calculates the breadth of a rectangle when given its perimeter and the acute angle between its diagonals. This geometric relationship helps determine the shorter side length based on the total boundary length and diagonal intersection angle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( b \) — Breadth of Rectangle (m)
• \( P \) — Perimeter of Rectangle (m)
• \( \theta \) — Acute Angle between Diagonals of Rectangle (°)
• \( \tan \) — Tangent trigonometric function

Explanation: The formula derives from the geometric properties of rectangles and trigonometric relationships between the sides and diagonals.

3. Importance of Breadth Calculation

Details: Calculating the breadth of a rectangle is essential in various fields including architecture, engineering, and design. It helps determine the dimensions of rectangular objects when the perimeter and diagonal angle are known.

4. Using the Calculator

Tips: Enter the perimeter in meters and the acute angle between diagonals in degrees. The angle must be between 0° and 90°. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid angle values?
A: The acute angle between diagonals must be between 0° and 90° (exclusive of 0° and inclusive of 90°).

Q2: Can this formula be used for squares?
A: Yes, for squares the acute angle between diagonals is 90°, and the formula will correctly calculate the side length.

Q3: What units should be used for input values?
A: Perimeter should be in meters and angle in degrees. The calculator will output breadth in meters.

Q4: How accurate is the calculation?
A: The calculation uses precise trigonometric functions and provides results accurate to 6 decimal places.

Q5: What if I have the obtuse angle between diagonals?
A: The acute angle is always the smaller angle between diagonals. If you have the obtuse angle, subtract it from 180° to get the acute angle.