Breadth of Rectangle given Perimeter and Angle between Diagonal and Length Calculator

Formula Used:

\[ b = \frac{P}{2} \times \frac{\tan(\angle_{dl})}{1 + \tan(\angle_{dl})} \]

Breadth of Rectangle:

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1. What is the Breadth of Rectangle Formula?

The formula calculates the breadth of a rectangle given its perimeter and the angle between the diagonal and the length. This relationship is derived from trigonometric properties of rectangles and their diagonals.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \frac{P}{2} \times \frac{\tan(\angle_{dl})}{1 + \tan(\angle_{dl})} \]

Where:

\( b \) — Breadth of Rectangle (m)
\( P \) — Perimeter of Rectangle (m)
\( \angle_{dl} \) — Angle between Diagonal and Length of Rectangle (radians)

Explanation: The formula utilizes trigonometric relationships between the rectangle's dimensions, perimeter, and the angle formed by its diagonal with the length side.

3. Importance of Rectangle Breadth Calculation

Details: Calculating the breadth of a rectangle is essential in geometry, architecture, engineering, and various design applications where precise dimensional relationships are required.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why use this specific formula for breadth calculation?
A: This formula provides a direct relationship between the perimeter, the angle between diagonal and length, and the breadth, making it efficient for calculations when these parameters are known.

Q2: What is the range of valid angle values?
A: The angle must be between 0° and 90° (exclusive) as these represent the possible angles between a rectangle's diagonal and its length side.

Q3: Can this formula be used for squares?
A: Yes, for a square (where length = breadth), the angle between the diagonal and length would be 45°, and the formula would yield the correct breadth value.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the trigonometric relationships in rectangles. The practical accuracy depends on the precision of the input values.

Q5: What are common applications of this calculation?
A: This calculation is useful in construction, manufacturing, graphic design, and any field requiring precise rectangular dimension calculations from known perimeter and angular relationships.