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

Formula Used:

\[ h = \sqrt{\frac{1}{\frac{1}{l_{Base2}^2 - l_{Right2}^2} + \frac{1}{l_{Right1}^2} + \frac{1}{l_{Right2}^2}} \]

Second Base Edge (l_Base2):

Second Right Angle Edge (l_Right2):

First Right Angle Edge (l_Right1):

Height of Trirectangular Tetrahedron (h):

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1. What is the Height of Trirectangular Tetrahedron?

The height of a trirectangular tetrahedron is the perpendicular distance from the vertex where the three right angles meet to the opposite face (the base). It represents the vertical dimension of this special tetrahedral shape.

2. How Does the Calculator Work?

The calculator uses the specific formula for height calculation:

\[ h = \sqrt{\frac{1}{\frac{1}{l_{Base2}^2 - l_{Right2}^2} + \frac{1}{l_{Right1}^2} + \frac{1}{l_{Right2}^2}} \]

Where:

\( h \) — Height of Trirectangular Tetrahedron (m)
\( l_{Base2} \) — Second Base Edge (m)
\( l_{Right2} \) — Second Right Angle Edge (m)
\( l_{Right1} \) — First Right Angle Edge (m)

Explanation: This formula calculates the height based on the geometric relationships between the base edge and the two right angle edges in a trirectangular tetrahedron.

3. Importance of Height Calculation

Details: Calculating the height is essential for determining the volume, understanding the spatial dimensions, and solving various geometric problems involving trirectangular tetrahedrons in 3D space.

4. Using the Calculator

Tips: Enter all edge lengths in meters. Ensure Second Base Edge > Second Right Angle Edge. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a trirectangular tetrahedron?
A: A trirectangular tetrahedron is a tetrahedron that has three faces meeting at one vertex at right angles to each other.

Q2: Why must Second Base Edge be greater than Second Right Angle Edge?
A: This condition ensures the mathematical validity of the formula and maintains geometric consistency in the tetrahedron's structure.

Q3: What are the units for the calculated height?
A: The height is calculated in meters (m), consistent with the input units for the edges.

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

Q5: How accurate is the calculation?
A: The calculation provides precise results based on the mathematical formula, with accuracy dependent on the precision of input values.