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This calculation determines the length of a rectangle when you know its circumradius (the radius of the circle that passes through all four vertices) and the angle between the diagonal and the breadth (width) 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 length relates to the diagonal through the sine of the angle between the diagonal and breadth.
Details: Calculating the length of a rectangle using circumradius and angle is important in geometry, engineering design, and architectural planning where these specific parameters might be known or easier to measure.
Tips: Enter the circumradius in meters and the angle in degrees (0-90°). The calculator automatically converts the angle to radians for the trigonometric calculation.
Q1: What is the circumradius of a rectangle?
A: The circumradius is half the length of the diagonal of the rectangle, which is the radius of the circle that passes through all four vertices.
Q2: Why use this formula instead of others?
A: This formula is useful when the circumradius and angle between diagonal and breadth are known, which might occur in certain geometric problems or practical measurements.
Q3: What is the range of valid angles?
A: The angle between diagonal and breadth must be between 0° and 90°, with 45° representing a square where length equals breadth.
Q4: Can this formula be used for all rectangles?
A: Yes, this formula applies to all rectangles, though the angle must be appropriately measured between the diagonal and the shorter side (breadth).
Q5: How accurate is this calculation?
A: The calculation is mathematically exact, but practical accuracy depends on the precision of the input measurements.