Obtuse Angle Between Diagonals Of Rectangle Given Angle Between Diagonal And Breadth Calculator

Formula Used:

\[ \text{Obtuse Angle between Diagonals of Rectangle} = 2 \times \text{Angle between Diagonal and Breadth of Rectangle} \] \[ \angle d_{\text{(Obtuse)}} = 2 \times \angle db \]

Obtuse Angle between Diagonals of Rectangle:

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1. What is Obtuse Angle between Diagonals of Rectangle?

The obtuse angle between diagonals of a rectangle is the larger angle formed where the two diagonals intersect. In any rectangle, the diagonals are equal in length and bisect each other, creating two pairs of equal angles - one acute and one obtuse.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \angle d_{\text{(Obtuse)}} = 2 \times \angle db \]

Where:

\( \angle d_{\text{(Obtuse)}} \) — Obtuse angle between diagonals (radians)
\( \angle db \) — Angle between diagonal and breadth of rectangle (radians)

Explanation: The obtuse angle between diagonals is exactly twice the angle formed between a diagonal and the breadth (shorter side) of the rectangle.

3. Importance of Obtuse Angle Calculation

Details: Calculating the obtuse angle between diagonals is important in geometry problems, architectural design, and various engineering applications where precise angle measurements are required for rectangular structures.

4. Using the Calculator

Tips: Enter the angle between the diagonal and breadth of the rectangle in radians. The value must be a positive number. The calculator will compute the corresponding obtuse angle between the diagonals.

5. Frequently Asked Questions (FAQ)

Q1: Why is the obtuse angle exactly twice the angle between diagonal and breadth?
A: Due to the geometric properties of rectangles and the fact that diagonals bisect each other and create congruent triangles, the obtuse angle between diagonals is always twice the angle between a diagonal and the breadth.

Q2: What is the range of possible values for the obtuse angle?
A: In a rectangle, the obtuse angle between diagonals ranges from more than 90 degrees to less than 180 degrees (or π/2 to π radians).

Q3: How does this relate to the acute angle between diagonals?
A: The acute and obtuse angles between diagonals are supplementary - they add up to 180 degrees (π radians).

Q4: Can this formula be used for other quadrilaterals?
A: This specific relationship only applies to rectangles. Other quadrilaterals have different angle relationships between their diagonals.

Q5: What if I have the angle in degrees instead of radians?
A: Convert degrees to radians first (radians = degrees × π/180) before using this calculator, or use a calculator that accepts degree input with automatic conversion.