Breadth of Rectangle given Perimeter and Angle between Diagonal and Breadth Calculator

Formula Used:

\[ b = \frac{P}{2 \times (1 + \tan(\angle_{db}))} \]

Breadth of Rectangle:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Breadth of Rectangle Formula?

The formula calculates the breadth of a rectangle when given its perimeter and the angle between the diagonal and the breadth. This geometric relationship helps determine the shorter side dimension of a rectangle using trigonometric principles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \frac{P}{2 \times (1 + \tan(\angle_{db}))} \]

Where:

\( b \) — Breadth of Rectangle (m)
\( P \) — Perimeter of Rectangle (m)
\( \angle_{db} \) — Angle between Diagonal and Breadth of Rectangle (°)

Explanation: The formula derives from the relationship between the rectangle's sides, perimeter, and the trigonometric tangent function applied to the angle between the diagonal and breadth.

3. Importance of Breadth Calculation

Details: Calculating the breadth is essential in various geometric applications, architectural designs, engineering projects, and mathematical problem-solving where rectangular dimensions need to be determined from given parameters.

4. Using the Calculator

Tips: Enter the perimeter in meters and the angle in degrees. The angle must be between 0° and 90°. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why use this specific formula for breadth calculation?
A: This formula provides a direct method to calculate the breadth when the perimeter and the angle between diagonal and breadth are known, using trigonometric relationships.

Q2: What are typical values for rectangle breadth?
A: The breadth can vary widely depending on the rectangle's proportions. In most practical applications, breadth values range from centimeters to meters.

Q3: How accurate is this calculation?
A: The calculation is mathematically precise when accurate input values are provided, as it's based on established geometric and trigonometric principles.

Q4: Are there limitations to this formula?
A: The formula assumes a perfect rectangle and requires the angle to be between 0° and 90°. It may not be applicable for degenerate cases or extremely small angles.

Q5: Can this formula be used for other quadrilateral shapes?
A: No, this specific formula applies only to rectangles due to their specific properties of equal opposite sides and right angles.