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The formula calculates the breadth of a rectangle using the diameter of its circumcircle and the angle between the diagonal and the breadth. This geometric relationship helps determine one dimension of the rectangle when the circumcircle and angle are known.
The calculator uses the formula:
Where:
Explanation: The formula utilizes trigonometric cosine function to relate the breadth of the rectangle to the diameter of its circumcircle and the angle between the diagonal and breadth.
Details: Calculating the breadth of a rectangle is essential in various geometric applications, construction projects, and engineering designs where precise dimensions are required.
Tips: Enter the diameter of the circumcircle in meters and the angle between diagonal and breadth in degrees. Both values must be positive, with angle between 0° and 90°.
Q1: What is a circumcircle of a rectangle?
A: A circumcircle is a circle that passes through all four vertices of the rectangle. For a rectangle, the diameter of the circumcircle equals the length of the diagonal.
Q2: Why use cosine function in this formula?
A: The cosine function relates the adjacent side (breadth) to the hypotenuse (diameter/diagonal) in the right triangle formed by the diagonal and sides of the rectangle.
Q3: Can this formula be used for squares?
A: Yes, since a square is a special type of rectangle, this formula applies to squares as well.
Q4: What are the measurement units for this calculation?
A: The calculator uses meters for length measurements and degrees for angles, but the formula works with any consistent unit system.
Q5: How accurate is this calculation?
A: The calculation is mathematically precise when correct values are input. The accuracy depends on the precision of the input measurements.