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

Formula Used:

\[ \text{Angle between Diagonal and Breadth of Rectangle} = \arctan\left(\frac{\text{Length of Rectangle}}{\left(\frac{\text{Perimeter of Rectangle}}{2}\right) - \text{Length of Rectangle}}\right) \] \[ \angle db = \arctan\left(\frac{l}{\left(\frac{P}{2}\right) - l}\right) \]

Angle between Diagonal and Breadth:

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1. What is Angle between Diagonal and Breadth of Rectangle?

The angle between diagonal and breadth of a rectangle is the acute angle formed between the diagonal and the shorter side (breadth) of the rectangle. This angle helps in understanding the geometric properties and proportions of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \angle db = \arctan\left(\frac{l}{\left(\frac{P}{2}\right) - l}\right) \]

Where:

\( \angle db \) — Angle between diagonal and breadth (degrees)
\( l \) — Length of the rectangle (m)
\( P \) — Perimeter of the rectangle (m)

Explanation: The formula calculates the angle using the inverse tangent function, relating the length to the derived breadth from the perimeter.

3. Importance of Angle Calculation

Details: Calculating this angle is important in geometry, engineering, and design applications where precise angular relationships in rectangular shapes are required.

4. Using the Calculator

Tips: Enter the length and perimeter of the rectangle. Both values must be positive numbers, and the perimeter must be greater than twice the length.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of possible angles?
A: The angle ranges from 0° to 90°, depending on the length-to-breadth ratio of the rectangle.

Q2: Can this calculator handle different units?
A: The calculator uses meters as default, but any consistent unit can be used as long as both inputs are in the same unit.

Q3: What if the perimeter is exactly twice the length?
A: This would mean breadth is zero, which is not a valid rectangle. The perimeter must be greater than twice the length.

Q4: How accurate is the calculation?
A: The calculation is mathematically precise based on the input values, with results rounded to 6 decimal places.

Q5: Can this formula be used for squares?
A: Yes, for a square (where length = breadth), the angle would be 45°.