Perimeter Of Rectangle Given Breadth And Angle Between Diagonal And Length Calculator

Formula Used:

\[ P = 2 \times b \times (1 + \cot(\angle_{dl})) \]

Perimeter of Rectangle:

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1. What is the Perimeter of Rectangle Formula?

The perimeter of a rectangle given breadth and angle between diagonal and length is calculated using the formula: P = 2 × b × (1 + cot(∠dl)). This formula provides an alternative method to calculate perimeter when the breadth and the angle between the diagonal and length are known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P = 2 \times b \times (1 + \cot(\angle_{dl})) \]

Where:

\( P \) — Perimeter of Rectangle (m)
\( b \) — Breadth of Rectangle (m)
\( \angle_{dl} \) — Angle between Diagonal and Length of Rectangle (degrees)
\( \cot \) — Cotangent trigonometric function

Explanation: The formula calculates the perimeter by using the breadth and the trigonometric relationship derived from the angle between the diagonal and the length of the rectangle.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a rectangle is essential in various fields including architecture, engineering, construction, and mathematics. It helps determine the total boundary length needed for fencing, framing, or material estimation.

4. Using the Calculator

Tips: Enter the breadth of the rectangle in meters and the angle between the diagonal and length in degrees. The angle must be between 0 and 90 degrees (exclusive). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid angle values?
A: The angle between diagonal and length must be between 0° and 90° (exclusive) for the formula to be valid.

Q2: How is the cotangent function calculated?
A: Cotangent is the reciprocal of tangent: cot(θ) = 1/tan(θ). The calculator automatically converts degrees to radians and computes the trigonometric function.

Q3: Can this formula be used for squares?
A: Yes, since a square is a special case of rectangle, this formula applies to squares as well.

Q4: What units should be used for inputs?
A: Breadth should be in meters, angle in degrees. The result will be in meters.

Q5: How accurate is the calculation?
A: The calculation provides results accurate to 6 decimal places, which is sufficient for most practical applications.