1. What Is The Diagonal Of Rectangle Given Breadth And Angle Between Diagonal And Length?

The diagonal of a rectangle can be calculated using the breadth and the angle between the diagonal and the length. This geometric relationship helps in determining the diagonal length when specific angle measurements are known.

2. How Does The Calculator Work?

The calculator uses the formula:

Where:

• \( d \) — Diagonal of Rectangle (m)
• \( b \) — Breadth of Rectangle (m)
• \( \angle_{dl} \) — Angle between Diagonal and Length of Rectangle (rad)
• \( \csc \) — Cosecant trigonometric function

Explanation: The formula utilizes trigonometric relationships in a rectangle, where the diagonal forms a right triangle with the sides of the rectangle.

3. Importance Of Diagonal Calculation

Details: Calculating the diagonal of a rectangle is important in various fields including architecture, engineering, and design, where precise measurements are crucial for structural integrity and aesthetic proportions.

4. Using The Calculator

Tips: Enter the breadth of the rectangle in meters and the angle between the diagonal and length in radians. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the cosecant function?
A: The cosecant function is the reciprocal of the sine function, defined as csc(θ) = 1/sin(θ).

Q2: Can I use degrees instead of radians?
A: The calculator requires angle input in radians. To convert degrees to radians, multiply by π/180.

Q3: What is the range of valid angle values?
A: The angle must be between 0 and π/2 radians (0-90 degrees) exclusive for a valid rectangle geometry.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the trigonometric relationship, assuming precise input values.

Q5: Can this formula be used for squares?
A: Yes, since a square is a special case of a rectangle, this formula applies to squares as well.