1. What is the Breadth of Rectangle given Circumradius and Angle between Diagonal and Breadth?

This formula calculates the breadth of a rectangle when you know its circumradius and the angle between the diagonal and the breadth. The circumradius is the radius of the circle that passes through all four vertices of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( b \) — Breadth of Rectangle (m)
• \( r_c \) — Circumradius of Rectangle (m)
• \( \angle_{db} \) — Angle between Diagonal and Breadth of Rectangle (rad)

Explanation: The formula uses trigonometric relationships in a rectangle to calculate the breadth based on the circumradius and the angle between the diagonal and breadth.

3. Importance of Breadth Calculation

Details: Calculating the breadth of a rectangle is essential in various geometric and engineering applications, particularly when working with circumscribed circles and angular relationships.

4. Using the Calculator

Tips: Enter the circumradius in meters and the angle in radians. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the circumradius of a rectangle?
A: The circumradius is the radius of the circle that passes through all four vertices of the rectangle. For a rectangle, it's equal to half the length of the diagonal.

Q2: How is the angle between diagonal and breadth measured?
A: The angle is measured in radians between the diagonal and the shorter side (breadth) of the rectangle.

Q3: Can this formula be used for squares?
A: Yes, since a square is a special type of rectangle, but the angle would be 45 degrees (π/4 radians) in that case.

Q4: What are the typical units for these measurements?
A: While meters are used here, any consistent unit system can be applied as long as all measurements use the same units.

Q5: What is the range of valid angles for this formula?
A: The angle should be between 0 and π/2 radians (0-90 degrees) for a valid rectangle configuration.