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

Formula Used:

\[ b = d \times \cos(\angle_{db}) \]

Breadth of Rectangle:

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1. What is the Breadth of Rectangle Formula?

The formula calculates the breadth of a rectangle when given its diagonal and the angle between the diagonal and the breadth. This geometric relationship is derived from trigonometric principles applied to the right triangle formed by the diagonal, length, and breadth of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = d \times \cos(\angle_{db}) \]

Where:

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

Explanation: The cosine function relates the adjacent side (breadth) to the hypotenuse (diagonal) in the right triangle formed by the diagonal and sides of the rectangle.

3. Importance of Breadth Calculation

Details: Calculating the breadth of a rectangle from its diagonal and angle is essential in various geometric applications, construction projects, and design calculations where complete measurements may not be directly available.

4. Using the Calculator

Tips: Enter the diagonal length in meters and the angle in degrees between 0-90. Both values must be positive numbers with the diagonal greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Why use cosine function in this calculation?
A: The cosine function relates the adjacent side (breadth) to the hypotenuse (diagonal) in a right triangle, making it the appropriate trigonometric function for this calculation.

Q2: What is the range of valid angle values?
A: The angle must be between 0° and 90° since it represents an acute angle in a right triangle formed by the rectangle's diagonal and sides.

Q3: Can this formula be used for any rectangle?
A: Yes, this formula applies to all rectangles as it's derived from fundamental geometric properties of rectangles and right triangles.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact when using precise input values, though real-world measurements may introduce some margin of error.

Q5: What if I know the length instead of the angle?
A: If you know the diagonal and length, you can calculate the breadth using the Pythagorean theorem: \( b = \sqrt{d^2 - l^2} \).