1. What is the Length of Rectangle Calculation?

This calculator determines the length of a rectangle when given its perimeter and the angle between the diagonal and the length. It uses trigonometric relationships to solve for the missing dimension.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The formula derives from the relationship between the rectangle's perimeter, its sides, and the trigonometric properties of the angle between the diagonal and length.

3. Importance of Length Calculation

Details: Calculating the length of a rectangle from its perimeter and diagonal angle is essential in geometry problems, architectural design, and various engineering applications where rectangular dimensions need to be determined from partial information.

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.

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 (non-inclusive of 0).

Q2: Why does the formula use tangent function?
A: The tangent function relates the opposite side (width) to the adjacent side (length) in the right triangle formed by the diagonal.

Q3: Can this calculator handle very large perimeter values?
A: Yes, the calculator can handle large values as long as they are within reasonable computational limits.

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

Q5: Is this calculation accurate for all rectangles?
A: Yes, this formula works for all rectangles as it's derived from fundamental geometric principles.