Breadth of Rectangle given Area and Obtuse Angle between Diagonals Calculator

Formula:

\[ b = \sqrt{\frac{A}{\tan\left(\frac{\angle_{d(Obtuse)}}{2}\right)}} \]

Breadth of Rectangle:

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1. What is the Breadth of Rectangle Formula?

The formula calculates the breadth of a rectangle when given its area and the obtuse angle between its diagonals. This geometric relationship helps determine the shorter side dimension based on the total area and diagonal intersection angle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \sqrt{\frac{A}{\tan\left(\frac{\angle_{d(Obtuse)}}{2}\right)}} \]

Where:

\( b \) — Breadth of Rectangle (m)
\( A \) — Area of Rectangle (m²)
\( \angle_{d(Obtuse)} \) — Obtuse Angle between Diagonals (degrees)

Explanation: The formula derives from trigonometric relationships between the rectangle's dimensions, area, and the angles formed by its diagonals.

3. Importance of Rectangle Breadth Calculation

Details: Calculating the breadth from area and diagonal angles is essential in geometry problems, architectural design, and various engineering applications where rectangular dimensions need to be determined from known properties.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle divided by 2 in the formula?
A: The diagonals of a rectangle bisect each other and create congruent triangles, so half the obtuse angle gives the appropriate trigonometric relationship.

Q2: What if I have the acute angle instead of the obtuse angle?
A: The acute and obtuse angles between diagonals are supplementary (sum to 180°), so you can calculate the obtuse angle if you know the acute one.

Q3: Can this formula be used for squares?
A: Yes, but for squares the diagonals intersect at 90° angles, making the calculation simpler as both length and breadth are equal.

Q4: What are the limitations of this formula?
A: The formula assumes a perfect rectangle and may not account for measurement errors in real-world applications.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for ideal rectangles, but real-world accuracy depends on the precision of your input measurements.