First Right Angle Edge of Trirectangular Tetrahedron given Third Base and Third Right Angle Edge Calculator

Formula Used:

\[ \text{First RA Edge} = \sqrt{\text{Third Base Edge}^2 - \text{Third RA Edge}^2} \]

First RA Edge:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the First Right Angle Edge of Trirectangular Tetrahedron?

The First Right Angle Edge of a Trirectangular Tetrahedron is the first edge out of the three mutually perpendicular edges. It plays a crucial role in defining the geometry and spatial relationships within the tetrahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{First RA Edge} = \sqrt{\text{Third Base Edge}^2 - \text{Third RA Edge}^2} \]

Where:

Third Base Edge — The third edge of the base acute triangular face (m)
Third RA Edge — The third mutually perpendicular edge (m)

Explanation: This formula derives from the Pythagorean theorem applied to the right-angled relationships within the tetrahedron.

3. Importance of First RA Edge Calculation

Details: Accurate calculation of the First RA Edge is essential for understanding the complete geometry of the trirectangular tetrahedron, which is important in various fields including crystallography, computational geometry, and 3D modeling.

4. Using the Calculator

Tips: Enter the Third Base Edge and Third RA Edge in meters. Both values must be positive, and the Third Base Edge must be greater than the Third RA Edge to obtain a valid result.

5. Frequently Asked Questions (FAQ)

Q1: What is a Trirectangular Tetrahedron?
A: A trirectangular tetrahedron is a tetrahedron where three faces meet at right angles at one vertex, creating three mutually perpendicular edges.

Q2: Why must the Third Base Edge be greater than the Third RA Edge?
A: This requirement ensures the expression under the square root remains positive, yielding a real number result for the First RA Edge.

Q3: Can this formula be applied to any tetrahedron?
A: No, this specific formula applies only to trirectangular tetrahedrons with the described geometric properties.

Q4: What units should I use for input values?
A: The calculator uses meters as the default unit, but the formula is unit-agnostic as long as consistent units are maintained.

Q5: How accurate is the calculated result?
A: The result is accurate to six decimal places, providing precision suitable for most engineering and mathematical applications.