Obtuse Angle between Diagonals of Rectangle given Perimeter and Breadth Calculator

Formula Used:

\[ \text{Obtuse Angle between Diagonals of Rectangle} = 2 \times \arctan\left(\frac{\left(\frac{\text{Perimeter of Rectangle}}{2}\right) - \text{Breadth of Rectangle}}{\text{Breadth of Rectangle}}\right) \]

\[ \angle d_{\text{(Obtuse)}} = 2 \times \arctan\left(\frac{\left(\frac{P}{2}\right) - b}{b}\right) \]

Obtuse Angle between Diagonals:

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1. What is Obtuse Angle between Diagonals of Rectangle?

The obtuse angle between diagonals of a rectangle is the angle greater than 90 degrees formed at the intersection point of the two diagonals. In a rectangle, the diagonals are equal in length and bisect each other, creating two acute angles and two obtuse angles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \angle d_{\text{(Obtuse)}} = 2 \times \arctan\left(\frac{\left(\frac{P}{2}\right) - b}{b}\right) \]

Where:

\( P \) — Perimeter of the rectangle
\( b \) — Breadth of the rectangle
\( \arctan \) — Inverse tangent function

Explanation: This formula calculates the obtuse angle between the diagonals based on the relationship between the perimeter and breadth of the rectangle.

3. Importance of Angle Calculation

Details: Calculating the angle between diagonals is important in geometry, engineering, and architectural design where precise angle measurements are required for structural integrity and aesthetic considerations.

4. Using the Calculator

Tips: Enter the perimeter and breadth of the rectangle in meters. Both values must be positive numbers. The calculator will compute the obtuse angle between the diagonals in degrees.

5. Frequently Asked Questions (FAQ)

Q1: Why are there both acute and obtuse angles between diagonals?
A: In a rectangle, diagonals intersect and create four angles - two acute angles and two obtuse angles that are supplementary to each other.

Q2: How does the perimeter relate to the angle between diagonals?
A: The perimeter, along with the breadth, helps determine the length of the rectangle, which affects the angle between the diagonals.

Q3: What is the range of possible obtuse angles?
A: In a rectangle, the obtuse angle between diagonals always ranges between 90° and 180°, typically around 120°-150° for most rectangles.

Q4: Can this formula be used for squares?
A: Yes, for a square (where length equals breadth), the formula will yield 135° as the obtuse angle between diagonals.

Q5: What units should be used for input values?
A: The calculator accepts any consistent units, but outputs angle in degrees. Ensure perimeter and breadth are in the same units.