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Obtuse Angle between Diagonals of Rectangle given Area and Breadth Calculator

Formula Used:

\[ \text{Obtuse Angle between Diagonals of Rectangle} = 2 \times \tan^{-1}\left(\frac{\text{Area of Rectangle}/\text{Breadth of Rectangle}}{\text{Breadth of Rectangle}}\right) \]

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1. What is the Obtuse Angle between Diagonals of Rectangle?

The Obtuse Angle between Diagonals of Rectangle is the angle greater than 90 degrees formed by the intersection of the two diagonals in a rectangle. This angle is complementary to the acute angle between the diagonals.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \angle_{d(Obtuse)} = 2 \times \tan^{-1}\left(\frac{A/b}{b}\right) \]

Where:

Explanation: The formula calculates the obtuse angle between diagonals using the area and breadth of the rectangle through trigonometric functions.

3. Importance of Obtuse Angle Calculation

Details: Calculating the angle between diagonals is important in geometry, engineering, and design applications where precise angular measurements are required for rectangular shapes.

4. Using the Calculator

Tips: Enter the area of the rectangle in square meters and the breadth in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of obtuse angle between diagonals?
A: The obtuse angle between diagonals of a rectangle always ranges between 90° and 180°.

Q2: How is this angle related to the acute angle?
A: The obtuse and acute angles between diagonals are supplementary, meaning they add up to 180°.

Q3: Can this formula be used for squares?
A: Yes, for squares (where length equals breadth), the formula will give the correct angle between diagonals.

Q4: What units should be used for inputs?
A: Consistent units should be used (e.g., meters for breadth, square meters for area). The result will be in degrees.

Q5: Are there any limitations to this formula?
A: This formula assumes a perfect rectangle and may not be accurate for irregular quadrilaterals or when inputs are invalid.

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