1. What is the Length of Rectangle given Area and Obtuse Angle between Diagonals Formula?

The formula calculates the length of a rectangle using its area and the obtuse angle between its diagonals. This geometric relationship helps determine one dimension of a rectangle when the area and diagonal angle are known.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l \) — Length of Rectangle (m)
• \( A \) — Area of Rectangle (m²)
• \( \angle_{d(Obtuse)} \) — Obtuse Angle between Diagonals (degrees)

Explanation: The formula derives from trigonometric relationships between rectangle dimensions, area, and diagonal angles.

3. Importance of Rectangle Length Calculation

Details: Calculating rectangle length from area and diagonal angle is important in geometry problems, architectural design, and various engineering applications where partial dimension information is available.

4. Using the Calculator

Tips: Enter area in square meters and obtuse angle between diagonals in degrees (must be between 90° and 180°). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle range restricted to 90°-180°?
A: The formula specifically calculates length using the obtuse angle between diagonals, which must be greater than 90° and less than or equal to 180°.

Q2: Can this formula be used for squares?
A: Yes, but for squares the diagonals always intersect at 90° angles, making the obtuse angle between diagonals 135°.

Q3: What if I know the acute angle instead?
A: The acute angle between diagonals is supplementary to the obtuse angle. You can calculate the obtuse angle by subtracting the acute angle from 180°.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of rectangles, given accurate input values.

Q5: Can this be used for other quadrilaterals?
A: No, this formula is specific to rectangles where all angles are 90° and diagonals are equal in length.