Angle Gamma Of Parallelepiped Calculator

Angle Gamma of Parallelepiped Formula:

\[ \angle\gamma = \asin\left(\frac{TSA - (2 \times S_b \times S_c \times \sin(\angle\alpha)) - (2 \times S_a \times S_c \times \sin(\angle\beta))}{2 \times S_b \times S_a}\right) \]

Total Surface Area of Parallelepiped:

m²

Side B of Parallelepiped:

Side C of Parallelepiped:

Angle Alpha of Parallelepiped:

rad

Side A of Parallelepiped:

Angle Beta of Parallelepiped:

rad

Angle Gamma of Parallelepiped:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Angle Gamma of Parallelepiped?

Angle Gamma of Parallelepiped is the angle formed by side A and side B at any of the two sharp tips of the Parallelepiped. It is one of the three important angles that define the shape and properties of a parallelepiped.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \angle\gamma = \asin\left(\frac{TSA - (2 \times S_b \times S_c \times \sin(\angle\alpha)) - (2 \times S_a \times S_c \times \sin(\angle\beta))}{2 \times S_b \times S_a}\right) \]

Where:

\( TSA \) — Total Surface Area of Parallelepiped (m²)
\( S_b \) — Side B of Parallelepiped (m)
\( S_c \) — Side C of Parallelepiped (m)
\( \angle\alpha \) — Angle Alpha of Parallelepiped (radians)
\( S_a \) — Side A of Parallelepiped (m)
\( \angle\beta \) — Angle Beta of Parallelepiped (radians)

Explanation: This formula calculates angle gamma based on the total surface area and the other known parameters of the parallelepiped.

3. Importance of Angle Gamma Calculation

Details: Calculating angle gamma is essential for understanding the complete geometric properties of a parallelepiped, which is important in fields like crystallography, computer graphics, and mechanical engineering where 3D shapes are analyzed.

4. Using the Calculator

Tips: Enter all values in the specified units. Angles should be in radians. Ensure all values are positive and the denominator in the formula doesn't become zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure formed by six parallelograms. It's the 3D equivalent of a parallelogram.

Q2: Why are angles important in a parallelepiped?
A: The three angles (alpha, beta, gamma) between the sides completely define the shape and proportions of a parallelepiped.

Q3: What are the valid ranges for the angles?
A: All angles in a parallelepiped must be between 0 and π radians (0° and 180°), but typically they are acute angles (less than 90°).

Q4: Can this calculator handle degrees instead of radians?
A: The calculator requires angles in radians, but the result is shown in both radians and degrees for convenience.

Q5: What if I get an error message?
A: Error messages typically indicate invalid input values that would result in mathematical errors like division by zero or values outside the domain of the inverse sine function.