Length Of Rectangle Given Diameter Of Circumcircle And Angle Between Diagonal And Length Calculator

Formula Used:

\[ l = D_c \times \cos(\angle dl) \]

Length of Rectangle (l):

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1. What is the Length of Rectangle Given Diameter of Circumcircle and Angle between Diagonal and Length?

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = D_c \times \cos(\angle dl) \]

Where:

\( l \) — Length of Rectangle (m)
\( D_c \) — Diameter of Circumcircle of Rectangle (m)
\( \angle dl \) — Angle between Diagonal and Length of Rectangle (rad)

Explanation: The formula uses the cosine trigonometric function to relate the diameter of the circumcircle (which equals the diagonal of the rectangle) and the angle between the diagonal and the length to calculate the actual length of the rectangle.

3. Importance of Length Calculation

Details: Calculating the length of a rectangle using geometric properties is essential in various fields including architecture, engineering, and design. It helps in determining dimensions when certain geometric constraints are known.

4. Using the Calculator

Tips: Enter the diameter of the circumcircle in meters and the angle in radians. The angle should be between 0 and π/2 radians (0-90 degrees). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why use this specific formula?
A: This formula provides a direct relationship between the circumcircle diameter (which equals the rectangle's diagonal) and the rectangle's length using trigonometric principles.

Q2: What is the range of valid angle values?
A: The angle should be between 0 and π/2 radians (0-90 degrees) as these are the possible angles between the diagonal and length in a rectangle.

Q3: How is the circumcircle related to the rectangle?
A: For any rectangle, all four vertices lie on a circle (circumcircle), and the diameter of this circle equals the diagonal of the rectangle.

Q4: 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.

Q5: What if I have the angle in degrees instead of radians?
A: You'll need to convert degrees to radians first (radians = degrees × π/180) before using the calculator.