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

Formula Used:

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

Length of Rectangle:

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1. What is the Length of Rectangle Formula?

This calculator determines the length of a rectangle when given its perimeter and the angle between the diagonal and the breadth. The formula uses trigonometric relationships to calculate the length based on these inputs.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( l \) — Length of Rectangle (m)
\( P \) — Perimeter of Rectangle (m)
\( \angle_{db} \) — Angle between Diagonal and Breadth of Rectangle (degrees)

Explanation: The formula derives from the geometric relationships in a rectangle, using trigonometric functions to relate the angle between the diagonal and breadth to the length and perimeter.

3. Importance of Length Calculation

Details: Calculating the length of a rectangle from its perimeter and angle information is useful in various geometric applications, construction projects, and design calculations where complete dimensions are not directly available.

4. Using the Calculator

Tips: Enter the perimeter in meters and the angle in degrees (between 0 and 90). Both values must be positive numbers. The angle represents the angle between the diagonal and the breadth of the rectangle.

5. Frequently Asked Questions (FAQ)

Q1: What is the valid range for the angle input?
A: The angle must be between 0 and 90 degrees, as these represent the possible angles between the diagonal and breadth in a rectangle.

Q2: Can this formula be used for squares?
A: Yes, but for squares (where length equals breadth), the angle between diagonal and breadth is always 45 degrees.

Q3: What units should I use for inputs?
A: The perimeter should be in meters, and the angle in degrees. The result will be in meters.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise based on the inputs. Ensure accurate measurement of both perimeter and angle for reliable results.

Q5: Can I use this for non-rectangular shapes?
A: No, this formula is specifically derived for rectangles and may not apply to other geometric shapes.