Area Of Rectangle Given Length And Obtuse Angle Between Diagonals Calculator

Area Of Rectangle Given Length And Obtuse Angle Between Diagonals Formula:

\[ A = l^2 \times \cot\left(\frac{\angle_{d(Obtuse)}}{2}\right) \]

Area of Rectangle:

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1. What is the Area of Rectangle Given Length and Obtuse Angle between Diagonals Formula?

The Area of Rectangle Given Length and Obtuse Angle between Diagonals formula calculates the area of a rectangle using its length and the obtuse angle between its diagonals. This approach provides an alternative method to calculate area when traditional length and width measurements are not available.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = l^2 \times \cot\left(\frac{\angle_{d(Obtuse)}}{2}\right) \]

Where:

\( A \) — Area of Rectangle (m²)
\( l \) — Length of Rectangle (m)
\( \angle_{d(Obtuse)} \) — Obtuse Angle between Diagonals of Rectangle (°)
\( \cot \) — Cotangent trigonometric function

Explanation: The formula utilizes the relationship between the rectangle's length, the angle between its diagonals, and trigonometric functions to calculate the area.

3. Importance of Area Calculation

Details: Calculating the area of a rectangle is fundamental in geometry and has practical applications in various fields including construction, architecture, land surveying, and material estimation.

4. Using the Calculator

Tips: Enter the length of the rectangle in meters and the obtuse angle between diagonals in degrees. The angle must be between 90° and 180° (exclusive). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why use this formula instead of length × width?
A: This formula is useful when you know the length and the angle between diagonals but don't have the width measurement available.

Q2: What is the range of valid angles for this formula?
A: The formula requires an obtuse angle between diagonals, which means the angle must be greater than 90° and less than 180°.

Q3: Can this formula be used for squares?
A: Yes, since a square is a special case of rectangle, this formula works for squares as well. For squares, the angle between diagonals is always 90°.

Q4: What units should be used for inputs?
A: Length should be in meters and angle in degrees. The calculator will automatically handle the conversion to radians for trigonometric calculations.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the inputs provided. The accuracy of the result depends on the accuracy of the input measurements.