Diagonal of Rectangle given Breadth and Obtuse Angle between Diagonals Calculator

Diagonal Of Rectangle Given Breadth And Obtuse Angle Between Diagonals Calculator

Formula Used:

\[ d = b \times \csc\left(\frac{\pi - \angle_{d(Obtuse)}}{2}\right) \]

Diagonal of Rectangle:

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1. What is the Diagonal of Rectangle Formula?

The formula calculates the diagonal length of a rectangle when given its breadth and the obtuse angle between the diagonals. This geometric relationship is derived from trigonometric principles applied to rectangle properties.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d = b \times \csc\left(\frac{\pi - \angle_{d(Obtuse)}}{2}\right) \]

Where:

\( d \) — Diagonal of Rectangle (m)
\( b \) — Breadth of Rectangle (m)
\( \angle_{d(Obtuse)} \) — Obtuse Angle between Diagonals (radians)
\( \pi \) — Mathematical constant pi (≈3.14159)
\( \csc \) — Cosecant trigonometric function

Explanation: The formula utilizes the cosecant function to relate the rectangle's breadth and the angle between diagonals to calculate the diagonal length.

3. Importance of Diagonal Calculation

Details: Calculating the diagonal of a rectangle is essential in various geometric applications, construction projects, and engineering designs where precise measurements of rectangular shapes are required.

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° (exclusive).

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle specified as obtuse?
A: In a rectangle, the diagonals always create two angles at their intersection - one acute and one obtuse. The formula specifically uses the obtuse angle for calculation.

Q2: What is the range of valid angle values?
A: The obtuse angle must be between 90° and 180° (exclusive of both endpoints) as these are the mathematical bounds for an obtuse angle in a rectangle.

Q3: Can this formula be used for squares?
A: Yes, since a square is a special case of rectangle, though the diagonals in a square create equal angles of 90° each.

Q4: What units should be used for inputs?
A: Breadth should be in meters, and angle in degrees. The calculator automatically converts degrees to radians for the trigonometric calculation.

Q5: How accurate is the calculation?
A: The calculation uses double-precision floating point arithmetic, providing results accurate to 6 decimal places for most practical applications.