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The Length of Wedge Cuboid given Long Diagonal is the length of the longer pair of edges of the base rectangular face of the Wedge Cuboid, calculated using the long diagonal, width, and long height of the Wedge Cuboid.
The calculator uses the formula:
Where:
Explanation: This formula is derived from the Pythagorean theorem applied in three dimensions, where the length is calculated as the square root of the difference between the square of the long diagonal and the squares of the width and long height.
Details: Calculating the length of a Wedge Cuboid is important in geometry and various engineering applications where precise measurements of three-dimensional objects are required for design and construction.
Tips: Enter the long diagonal, width, and long height in meters. All values must be positive and valid (greater than 0). Ensure that the input values satisfy the condition \( d_{Long}^2 > w^2 + h_{Long}^2 \) for a real solution.
Q1: What is a Wedge Cuboid?
A: A Wedge Cuboid is a three-dimensional geometric shape with a rectangular base and a sloping top face, resembling a wedge.
Q2: Why is the square root function used in the formula?
A: The square root function is used to solve for the length from the squared terms in the Pythagorean theorem applied in three dimensions.
Q3: What units should be used for input values?
A: The calculator uses meters (m) for all input values. Ensure consistent units for accurate results.
Q4: What if the calculated length is imaginary?
A: If \( d_{Long}^2 < w^2 + h_{Long}^2 \), the length would be imaginary, indicating that the input values do not form a valid Wedge Cuboid with the given dimensions.
Q5: Can this formula be used for other shapes?
A: This specific formula is tailored for Wedge Cuboids. Other shapes may require different formulas based on their geometric properties.