Obtuse Angle between Diagonals of Rectangle given Diagonal and Breadth Calculator

Formula Used:

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

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 any rectangle, the diagonals intersect each other and create two acute angles and two obtuse angles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Obtuse Angle} = 2 \times \arccos\left(\frac{b}{d}\right) \]

Where:

\( b \) — Breadth of Rectangle (m)
\( d \) — Diagonal of Rectangle (m)
\( \arccos \) — Inverse cosine function

Explanation: The formula calculates the obtuse angle between diagonals based on the ratio of breadth to diagonal length using trigonometric relationships.

3. Importance of Angle Calculation

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

4. Using the Calculator

Tips: Enter the breadth and diagonal of the rectangle in meters. Both values must be positive numbers, and the breadth must be less than the diagonal for valid results.

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle between diagonals always obtuse?
A: In a rectangle, the diagonals intersect to form two acute angles and two obtuse angles. The obtuse angle is calculated using this formula.

Q2: What is the range of possible obtuse angles?
A: The obtuse angle between diagonals of a rectangle ranges from 90° to 180°, but typically falls between 90° and 180° depending on the rectangle's proportions.

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

Q4: Can this formula be used for squares?
A: Yes, for a square (where breadth equals length), the diagonals intersect at 90-degree angles, making both acute and obtuse angles equal to 90 degrees.

Q5: What units should be used for inputs?
A: The calculator uses meters, but any consistent unit of length can be used as the ratio remains the same.