Perimeter of Rectangle given Breadth and Obtuse Angle between Diagonals Calculator

Formula Used:

\[ P = 2 \times b \times \left(1 + \cot\left(\frac{\pi - \angle_{d(Obtuse)}}{2}\right)\right) \]

Perimeter of Rectangle:

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1. What is the Perimeter of Rectangle?

The perimeter of a rectangle is the total length of all its four sides. It represents the distance around the outer boundary of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P = 2 \times b \times \left(1 + \cot\left(\frac{\pi - \angle_{d(Obtuse)}}{2}\right)\right) \]

Where:

\( P \) — Perimeter of Rectangle (m)
\( b \) — Breadth of Rectangle (m)
\( \angle_{d(Obtuse)} \) — Obtuse Angle between Diagonals (radians)
\( \pi \) — Archimedes' constant (≈ 3.14159)
\( \cot \) — Cotangent trigonometric function

Explanation: This formula calculates the perimeter of a rectangle when the breadth and the obtuse angle between its diagonals are known, using trigonometric relationships.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a rectangle is essential in various fields including construction, architecture, land surveying, and manufacturing. It helps determine the amount of material needed for fencing, framing, or bordering rectangular areas.

4. Using the Calculator

Tips: Enter the breadth of the rectangle in meters and the obtuse angle between diagonals in degrees. The angle must be between 90° and 180°. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why use this specific formula for perimeter calculation?
A: This formula is particularly useful when you know the breadth of the rectangle and the obtuse angle between its diagonals, allowing you to calculate the perimeter without knowing the length.

Q2: What is the range of valid angles for this calculation?
A: The obtuse angle between diagonals must be between 90° and 180° (inclusive), as this formula specifically handles the obtuse angle case.

Q3: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values. The accuracy of the result depends on the precision of your input measurements.

Q4: Can this formula be used for squares?
A: Yes, since a square is a special case of rectangle, this formula works for squares as well. For a square, the obtuse angle between diagonals is 135°.

Q5: What if I know the acute angle instead of the obtuse angle?
A: The acute angle between diagonals is supplementary to the obtuse angle (they add up to 180°). You can convert the acute angle to obtuse by subtracting it from 180°.