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This calculation determines the length of a rectangle using its circumradius and the angle between the diagonal and the length. The circumradius is the radius of the circle that passes through all four vertices of the rectangle.
The calculator uses the formula:
Where:
Explanation: The formula derives from trigonometric relationships in a rectangle, where the diagonal equals twice the circumradius, and the cosine of the angle relates the length to the diagonal.
Details: Calculating the length of a rectangle using circumradius and angle is essential in geometry, engineering, and design applications where these parameters are known, and the dimensions of the rectangle need to be determined.
Tips: Enter the circumradius in meters and the angle in radians. The angle should be between 0 and π/2 radians (0-90 degrees). All values must be positive.
Q1: What is the circumradius of a rectangle?
A: The circumradius is the radius of the circumscribed circle that passes through all four vertices of the rectangle. It equals half the length of the diagonal.
Q2: Why use cosine in this formula?
A: The cosine function relates the adjacent side (length) to the hypotenuse (diagonal) in the right triangle formed by the length, width, and diagonal of the rectangle.
Q3: Can this formula be used for squares?
A: Yes, for a square, the angle between the diagonal and any side is 45 degrees (π/4 radians), and the formula will correctly calculate the side length.
Q4: What are the limitations of this calculation?
A: The angle must be between 0 and 90 degrees (0 and π/2 radians). The circumradius must be positive and greater than zero.
Q5: How is this formula derived?
A: The formula comes from the relationship between the diagonal (d = 2×r_c), and the trigonometric identity: length = diagonal × cos(angle).