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This calculation determines the length of a rectangle when you know the diameter of its circumcircle and the obtuse angle between its diagonals. The circumcircle is the circle that passes through all four vertices of the rectangle.
The calculator uses the formula:
Where:
Explanation: The formula uses trigonometric relationships between the rectangle's dimensions, its circumcircle diameter, and the angle between its diagonals.
Details: Calculating rectangle dimensions from geometric properties is essential in various fields including engineering, architecture, and computer graphics where precise measurements are required.
Tips: Enter the diameter of the circumcircle in meters and the obtuse angle between diagonals in degrees (must be between 90° and 180°). All values must be positive and valid.
Q1: What is a circumcircle of a rectangle?
A: A circumcircle is a circle that passes through all four vertices of a rectangle. For any rectangle, the circumcircle's center is at the intersection point of the diagonals.
Q2: Why is the angle between diagonals important?
A: The angle between diagonals affects the aspect ratio of the rectangle. The obtuse angle (greater than 90°) and its complementary acute angle together determine the rectangle's length and width proportions.
Q3: Can this formula be used for squares?
A: Yes, for squares the obtuse angle between diagonals is 135°, and the formula will correctly calculate the side length.
Q4: What are practical applications of this calculation?
A: This calculation is useful in structural design, computer-aided design (CAD), and geometric problem-solving where rectangle dimensions need to be determined from known geometric properties.
Q5: How accurate is this calculation?
A: The calculation is mathematically precise when using exact inputs. The accuracy of the result depends on the precision of the input values.