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

The angle between the diagonal and length of a rectangle is the acute 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:

Where:

• \( \angle dl \) — Angle between diagonal and length (degrees)
• \( b \) — Breadth of the rectangle (m)
• \( r_c \) — Circumradius of the rectangle (m)

Explanation: The formula calculates the angle using the inverse sine function, relating the breadth to twice the circumradius of the rectangle.

3. Importance of Angle Calculation

Details: Calculating this angle is important in geometry, engineering, and design applications where precise angular relationships in rectangular shapes are required.

4. Using the Calculator

Tips: Enter the breadth and circumradius values in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of possible values for this angle?
A: The angle ranges from 0° to 45°, where 0° occurs when breadth is 0, and 45° occurs when the rectangle is a square.

Q2: How is circumradius related to rectangle dimensions?
A: The circumradius is half the length of the diagonal: \( r_c = \frac{\sqrt{l^2 + b^2}}{2} \), where l is length and b is breadth.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. Ensure consistent units for both inputs to get correct results.

Q4: What if I get an error in calculation?
A: Make sure the circumradius is at least half the breadth, as the formula requires \( 2 \times r_c \geq b \) for valid results.

Q5: How accurate is the calculated angle?
A: The calculator provides results with 4 decimal places precision, suitable for most practical applications.