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The formula calculates the breadth of a rectangle given its length and the angle between the diagonal and the length. This trigonometric approach provides an alternative method to determine rectangle dimensions when angle information is available.
The calculator uses the formula:
Where:
Explanation: The formula uses the tangent trigonometric function to relate the angle between the diagonal and length to the ratio of breadth to length in a right triangle formed by the rectangle's dimensions.
Details: Understanding rectangle geometry and trigonometric relationships is crucial for various applications in mathematics, engineering, architecture, and design where precise dimensional calculations are required.
Tips: Enter the length in meters and the angle in degrees. The angle must be between 0° and 90° (exclusive). All values must be positive numbers.
Q1: Why use this formula instead of other methods?
A: This formula provides a direct calculation of breadth when the length and angle between diagonal and length are known, which can be useful in trigonometric applications.
Q2: What is the range of valid angle values?
A: The angle must be between 0° and 90° (exclusive) for the tangent function to produce valid results.
Q3: Can this formula be used for squares?
A: Yes, for squares where length equals breadth, the angle between diagonal and length would be 45°.
Q4: What are the limitations of this approach?
A: The formula assumes precise angle measurement and may be less accurate for very small angles where tangent values approach infinity.
Q5: How is this formula derived?
A: The formula is derived from the trigonometric relationship in the right triangle formed by the length, breadth, and diagonal of the rectangle.