Angle Between Diagonal and Length of Rectangle Given Area and Breadth Calculator

Formula Used:

\[ \text{Angle between Diagonal and Length of Rectangle} = \arctan\left(\frac{\text{Breadth of Rectangle}}{\frac{\text{Area of Rectangle}}{\text{Breadth of Rectangle}}}\right) \] \[ \angle dl = \arctan\left(\frac{b}{\frac{A}{b}}\right) \]

Angle between Diagonal and Length:

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1. What is the Angle Between Diagonal and Length of Rectangle?

The angle between the diagonal and length of a rectangle is the measure of the angle formed between the diagonal and the longer side (length) of the rectangle. This angle helps in understanding the geometric properties and proportions of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \angle dl = \arctan\left(\frac{b}{\frac{A}{b}}\right) \]

Where:

\( \angle dl \) — Angle between diagonal and length (degrees)
\( b \) — Breadth of the rectangle (m)
\( A \) — Area of the rectangle (m²)

Explanation: The formula calculates the angle using the arctangent function based on the relationship between the breadth and the derived length (from area/breadth) of the rectangle.

3. Importance of Angle Calculation

Details: Calculating this angle is important in various fields such as architecture, engineering, and design where precise angular measurements are required for construction and analysis.

4. Using the Calculator

Tips: Enter the breadth and area of the rectangle. Both values must be positive numbers. The calculator will compute the angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for inputs?
A: Use consistent units (e.g., meters for breadth and square meters for area). The angle result is in degrees.

Q2: Can the angle be greater than 90 degrees?
A: No, in a rectangle, the angle between the diagonal and length is always between 0 and 90 degrees.

Q3: What if I have the length instead of area?
A: If you have the length, you can directly use the formula: angle = arctan(breadth/length).

Q4: How accurate is the calculation?
A: The calculation is mathematically precise based on the inputs. Ensure accurate measurements for correct results.

Q5: Can this calculator be used for squares?
A: Yes, for a square (where breadth = length), the angle will be 45 degrees.