Diagonal Of Rectangle Given Area And Angle Between Diagonal And Length Calculator

Formula Used:

\[ d = \frac{\sqrt{A \cdot \cot(\angle_{dl})}}{\cos(\angle_{dl})} \]

Diagonal of Rectangle (d):

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1. What is the Diagonal of Rectangle Formula?

The formula calculates the diagonal length of a rectangle when given the area and the angle between the diagonal and the length of the rectangle. This geometric relationship helps determine the spatial dimensions of rectangular objects.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d = \frac{\sqrt{A \cdot \cot(\angle_{dl})}}{\cos(\angle_{dl})} \]

Where:

\( d \) — Diagonal of the rectangle (m)
\( A \) — Area of the rectangle (m²)
\( \angle_{dl} \) — Angle between diagonal and length (degrees)
\( \cot \) — Cotangent trigonometric function
\( \cos \) — Cosine trigonometric function

Explanation: The formula combines trigonometric relationships with geometric properties to calculate the diagonal length based on the given area and angle.

3. Importance of Diagonal Calculation

Details: Calculating the diagonal of a rectangle is important in various fields including architecture, engineering, and design. It helps determine the maximum span within a rectangular space and is crucial for structural calculations.

4. Using the Calculator

Tips: Enter the area in square meters and the angle in degrees (between 0 and 90). Both values must be positive numbers. The angle represents the angle between the diagonal and the length side of the rectangle.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid angle values?
A: The angle must be between 0 and 90 degrees (exclusive). At 0 degrees, the rectangle would have zero width, and at 90 degrees, it would have zero length.

Q2: Can this formula be used for squares?
A: Yes, for squares where length equals width, the angle between diagonal and length is 45 degrees.

Q3: What units should I use for the area?
A: The calculator uses square meters, but you can use any consistent unit system as long as the diagonal result will be in the corresponding linear unit.

Q4: How accurate is the calculation?
A: The calculation is mathematically precise based on the input values. The result is rounded to 6 decimal places for clarity.

Q5: What if I know the length and width instead?
A: If you know both length and width, you can calculate the diagonal directly using the Pythagorean theorem: \( d = \sqrt{l^2 + w^2} \).