Length of Rectangle given Perimeter and Obtuse Angle between Diagonals Calculator

Formula Used:

\[ l = \frac{P}{2} \times \frac{\tan\left(\frac{\angle_{d(Obtuse)}}{2}\right)}{1 + \tan\left(\frac{\angle_{d(Obtuse)}}{2}\right)} \]

Length of Rectangle:

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1. What is the Length of Rectangle given Perimeter and Obtuse Angle between Diagonals?

This calculation determines the length of a rectangle when you know its total perimeter and the obtuse angle between its diagonals. The length is one of the fundamental dimensions that defines the size and proportions of a rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = \frac{P}{2} \times \frac{\tan\left(\frac{\angle_{d(Obtuse)}}{2}\right)}{1 + \tan\left(\frac{\angle_{d(Obtuse)}}{2}\right)} \]

Where:

\( l \) — Length of Rectangle (m)
\( P \) — Perimeter of Rectangle (m)
\( \angle_{d(Obtuse)} \) — Obtuse Angle between Diagonals of Rectangle (°)

Explanation: The formula uses trigonometric relationships derived from the geometry of rectangles and their diagonals to calculate the length based on the given perimeter and diagonal angle.

3. Importance of Length Calculation

Details: Calculating the length of a rectangle is essential in various fields including architecture, engineering, design, and mathematics. It helps in determining the exact dimensions needed for construction, manufacturing, and spatial planning.

4. Using the Calculator

Tips: Enter the perimeter in meters and the obtuse angle between diagonals in degrees. The angle must be between 90° and 180° (exclusive of 90°, inclusive of 180°). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle restricted to obtuse angles?
A: In a rectangle, the diagonals always create one acute and one obtuse angle. The obtuse angle is used in this specific calculation.

Q2: What if I have the acute angle instead?
A: You can convert the acute angle to obtuse by subtracting it from 180°, since the two angles between diagonals are supplementary.

Q3: Can this formula be used for squares?
A: Yes, but in a square the diagonals intersect at right angles (90°), so both angles between diagonals are 90°, which is not obtuse.

Q4: What are practical applications of this calculation?
A: This is useful in construction, furniture design, packaging, and any field where rectangular dimensions need to be calculated from known perimeter and diagonal angles.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of rectangles. The accuracy of the result depends on the precision of the input values.