Height of Trirectangular Tetrahedron given First Base and Second Right Angle Edge Calculator

Formula Used:

\[ h = \sqrt{\frac{1}{\frac{1}{l_{Base1}^2 - l_{Right2}^2} + \frac{1}{l_{Right2}^2} + \frac{1}{l_{Right3}^2}} \]

Height of Trirectangular Tetrahedron (h):

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1. What is Height of Trirectangular Tetrahedron?

The height of a trirectangular tetrahedron is the vertical distance from the acute triangular face to the opposite corner where the three right angle edges meet. It represents the perpendicular distance between these two geometric elements.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \sqrt{\frac{1}{\frac{1}{l_{Base1}^2 - l_{Right2}^2} + \frac{1}{l_{Right2}^2} + \frac{1}{l_{Right3}^2}} \]

Where:

\( h \) — Height of Trirectangular Tetrahedron (m)
\( l_{Base1} \) — First Base Edge (m)
\( l_{Right2} \) — Second RA Edge (m)
\( l_{Right3} \) — Third RA Edge (m)

Explanation: The formula calculates the height based on the geometric relationships between the base edge and the right angle edges of the tetrahedron.

3. Importance of Height Calculation

Details: Calculating the height of a trirectangular tetrahedron is essential for understanding its spatial properties, volume calculations, and various engineering applications involving three-dimensional geometry.

4. Using the Calculator

Tips: Enter all edge lengths in meters. Ensure all values are positive and that the First Base Edge is greater than the Second RA Edge for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is a trirectangular tetrahedron?
A: A trirectangular tetrahedron is a tetrahedron with three faces meeting at one vertex that are mutually perpendicular to each other.

Q2: Why must the First Base Edge be greater than the Second RA Edge?
A: This condition ensures that the term \( l_{Base1}^2 - l_{Right2}^2 \) remains positive, which is mathematically necessary for the formula to produce real number results.

Q3: What are typical applications of this calculation?
A: This calculation is used in 3D modeling, architectural design, structural engineering, and various geometric analysis applications.

Q4: Can this formula be used for any tetrahedron?
A: No, this specific formula applies only to trirectangular tetrahedrons with the given geometric properties.

Q5: How accurate are the results from this calculator?
A: The results are mathematically precise based on the input values, with rounding to 6 decimal places for practical use.