Obtuse Angle between Diagonals of Rectangle given Perimeter and Length Calculator

Formula Used:

\[ \text{Obtuse Angle between Diagonals of Rectangle} = 2 \times \tan^{-1}\left(\frac{\text{Length of Rectangle}}{\left(\frac{\text{Perimeter of Rectangle}}{2}\right) - \text{Length of Rectangle}}\right) \] \[ \angle d_{\text{(Obtuse)}} = 2 \times \tan^{-1}\left(\frac{l}{\left(\frac{P}{2}\right) - l}\right) \]

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 Rectangle is the angle greater than 90 degrees formed by the intersection of the two diagonals of a rectangle. In any rectangle, the diagonals intersect and create two pairs of angles - one acute and one obtuse.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \angle d_{\text{(Obtuse)}} = 2 \times \tan^{-1}\left(\frac{l}{\left(\frac{P}{2}\right) - l}\right) \]

Where:

\( \angle d_{\text{(Obtuse)}} \) — Obtuse angle between diagonals (degrees)
\( l \) — Length of the rectangle (m)
\( P \) — Perimeter of the rectangle (m)

Explanation: This formula derives from the geometric properties of rectangles and trigonometric relationships between the sides and angles formed by the diagonals.

3. Importance of Angle Calculation

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

4. Using the Calculator

Tips: Enter the length and perimeter of the rectangle. Both values must be positive numbers, and the perimeter must be greater than twice the length for a valid rectangle.

5. Frequently Asked Questions (FAQ)

Q1: Why is there both an acute and obtuse angle between diagonals?
A: The diagonals of a rectangle intersect and create four angles. Two are acute (less than 90°) and two are obtuse (greater than 90°), with the acute and obtuse angles being supplementary.

Q2: What is the relationship between the two angles?
A: The acute and obtuse angles between the diagonals always sum to 180 degrees, as they form a linear pair.

Q3: Does this formula work for squares?
A: Yes, for squares (where length equals width), the formula will correctly calculate 90 degrees for both angles, since in a square all angles between diagonals are equal to 90 degrees.

Q4: What are the practical applications of this calculation?
A: This calculation is used in construction, carpentry, graphic design, and any field where precise angular measurements of rectangular objects are needed.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values. The accuracy of the result depends on the precision of the input measurements.