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

Formula Used:

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

Third RA Edge:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Third RA Edge of Trirectangular Tetrahedron?

The Third Right Angle (RA) Edge of a Trirectangular Tetrahedron is the third edge out of the three mutually perpendicular edges. It is calculated based on the relationship between the second base edge and the second right angle edge using the Pythagorean theorem.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

Second Base Edge — The second edge of the base acute triangular face (in meters)
Second RA Edge — The second mutually perpendicular edge (in meters)

Explanation: This formula is derived from the Pythagorean theorem, applied to the right-angled relationships within the trirectangular tetrahedron.

3. Importance of Third RA Edge Calculation

Details: Calculating the Third RA Edge is essential for determining the complete set of mutually perpendicular edges in a trirectangular tetrahedron, which is fundamental in geometric analysis and 3D modeling.

4. Using the Calculator

Tips: Enter the Second Base Edge and Second RA Edge in meters. Ensure that the Second Base Edge is greater than the Second RA Edge, and both values are positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a Trirectangular Tetrahedron?
A: A trirectangular tetrahedron is a tetrahedron with three faces that are mutually perpendicular and right-angled at one vertex.

Q2: Why must the Second Base Edge be greater than the Second RA Edge?
A: Because the formula involves taking the square root of the difference of squares, which requires the square of the Second Base Edge to be larger to avoid imaginary results.

Q3: Can this formula be used for any right-angled tetrahedron?
A: This specific formula applies to trirectangular tetrahedrons where the edges are mutually perpendicular and follow the given relationship.

Q4: What units should be used?
A: The calculator uses meters, but the formula is unit-agnostic as long as consistent units are used for both inputs.

Q5: What if the inputs are invalid?
A: The calculator will display an error message if the Second Base Edge is not greater than the Second RA Edge, or if either value is non-positive.