Diagonal of Rectangle given Length and Obtuse Angle between Diagonals Calculator

Formula Used:

\[ d = \frac{l}{\cos\left(\frac{\pi - \angle_{d(Obtuse)}}{2}\right)} \]

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 the length of one side 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:

\[ d = \frac{l}{\cos\left(\frac{\pi - \angle_{d(Obtuse)}}{2}\right)} \]

Where:

\( d \) — Diagonal of Rectangle (m)
\( l \) — Length of Rectangle (m)
\( \angle_{d(Obtuse)} \) — Obtuse Angle between Diagonals (radians)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \cos \) — Cosine trigonometric function

Explanation: The formula utilizes trigonometric relationships in the right triangles formed by the diagonals within the rectangle, considering the supplementary nature of the acute and obtuse angles between diagonals.

3. Importance of Diagonal Calculation

Details: Calculating the diagonal of a rectangle is essential in various fields including architecture, engineering, and computer graphics. It helps determine the maximum distance between opposite corners and is crucial for structural analysis and design optimization.

4. Using the Calculator

Tips: Enter the length of the rectangle in meters and the obtuse angle between diagonals in degrees (must be between 90° and 180°). Both values must be positive numbers with appropriate ranges.

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle converted from degrees to radians?
A: Trigonometric functions in mathematical calculations typically use radians as the standard unit of measurement for angles.

Q2: What is the range of valid angle values?
A: The obtuse angle between diagonals must be between 90° and 180° (inclusive) as this formula specifically handles obtuse angles.

Q3: Can this formula be used for squares?
A: Yes, since a square is a special case of rectangle, though the angle between diagonals in a square is always 90° (right angle), not obtuse.

Q4: What if I know the width instead of the length?
A: The formula can be adapted by using trigonometric relationships, but this specific implementation requires the length measurement.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values, with results rounded to 6 decimal places for practical use.