1. What is the Diagonal of Rectangle Formula?

The diagonal of a rectangle can be calculated using the length and the angle between the diagonal and the breadth. This formula provides an alternative method to the Pythagorean theorem for finding the diagonal length.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( d \) — Diagonal of the rectangle (m)
• \( l \) — Length of the rectangle (m)
• \( \angle_{db} \) — Angle between diagonal and breadth (degrees)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)
• \( \sec \) — Secant trigonometric function

Explanation: The formula uses trigonometric relationships to calculate the diagonal length based on the given angle and the rectangle's length.

3. Importance of Diagonal Calculation

Details: Calculating the diagonal of a rectangle is important in various fields including geometry, engineering, architecture, and construction. It helps in determining the longest straight-line distance within the rectangle.

4. Using the Calculator

Tips: Enter the length of the rectangle in meters and the angle between the diagonal and breadth in degrees (0-90°). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between this formula and the Pythagorean theorem?
A: Both methods calculate the diagonal, but this trigonometric approach uses angle measurements instead of both side lengths.

Q2: What range of angles is valid for this calculation?
A: The angle between diagonal and breadth must be between 0° and 90° for a valid rectangle.

Q3: Can this formula be used for squares?
A: Yes, squares are a special case of rectangles, so this formula applies to squares as well.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise when using exact trigonometric values and proper angle measurements.

Q5: What units should be used for the inputs?
A: Length should be in meters, and angle in degrees. The calculator will output the diagonal in meters.