1. What is the Circumradius of Rectangle?

The circumradius of a rectangle is the radius of the circle which contains the rectangle with all the vertices of the rectangle lying on the circle. For any rectangle, the circumradius is equal to half the length of the diagonal.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumradius of Rectangle (m)
• \( l \) — Length of Rectangle (m)
• \( \angle dl \) — Angle between Diagonal and Length of Rectangle (radians)
• \( \sec \) — Secant trigonometric function

Explanation: The formula calculates the circumradius using the length of the rectangle and the angle between the diagonal and the length, applying trigonometric relationships.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry, engineering, and design applications where circular constraints or circumscribed circles around rectangular shapes are involved.

4. Using the Calculator

Tips: Enter the length of the rectangle in meters and the angle between the diagonal and length in degrees. All values must be valid (length > 0, angle between 0-90°).

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between circumradius and diagonal?
A: The circumradius of a rectangle is exactly half the length of its diagonal.

Q2: Can this formula be used for squares?
A: Yes, since a square is a special case of a rectangle, this formula applies to squares as well.

Q3: What is the range of valid angle values?
A: The angle between the diagonal and length must be between 0° and 90°, exclusive.

Q4: How is the secant function calculated?
A: The secant function is the reciprocal of the cosine function: sec(θ) = 1/cos(θ).

Q5: What units should I use for the inputs?
A: Length should be in meters, and angle should be in degrees. The calculator will convert the angle to radians internally.