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Angle Gamma of Parallelepiped Formula

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Angle Gamma of Parallelepiped is the angle formed by side A and side B at any of the two sharp tips of the Parallelepiped. Check FAQs

∠γ = a \sin (\frac{TSA - (2 \cdot S b \cdot S c \cdot \sin (∠α)) - (2 \cdot S a \cdot S c \cdot \sin (∠β))}{2 \cdot S b \cdot S a})

∠γ - Angle Gamma of Parallelepiped?TSA - Total Surface Area of Parallelepiped?S_b - Side B of Parallelepiped?S_c - Side C of Parallelepiped?∠α - Angle Alpha of Parallelepiped?S_a - Side A of Parallelepiped?∠β - Angle Beta of Parallelepiped?

Angle Gamma of Parallelepiped Example

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Here is how the Angle Gamma of Parallelepiped equation looks like with Values.

Here is how the Angle Gamma of Parallelepiped equation looks like with Units.

Here is how the Angle Gamma of Parallelepiped equation looks like.

74.7132 = a \sin (\frac{1960 - (2 \cdot 20 \cdot 10 \cdot \sin (45)) - (2 \cdot 30 \cdot 10 \cdot \sin (60))}{2 \cdot 20 \cdot 30})

74.7132° = a \sin (\frac{1960m² - (2 \cdot 20m \cdot 10m \cdot \sin (45°)) - (2 \cdot 30m \cdot 10m \cdot \sin (60°))}{2 \cdot 20m \cdot 30m})

74.7132 = a \sin (\frac{1960 - (2 \cdot 20 \cdot 10 \cdot \sin (45)) - (2 \cdot 30 \cdot 10 \cdot \sin (60))}{2 \cdot 20 \cdot 30})

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Angle Gamma of Parallelepiped Solution

Follow our step by step solution on how to calculate Angle Gamma of Parallelepiped?

FIRST Step Consider the formula

∠γ = a \sin (\frac{TSA - (2 \cdot S b \cdot S c \cdot \sin (∠α)) - (2 \cdot S a \cdot S c \cdot \sin (∠β))}{2 \cdot S b \cdot S a})

Next Step Substitute values of Variables

∴

∠γ = a \sin (\frac{1960m² - (2 \cdot 20m \cdot 10m \cdot \sin (45°)) - (2 \cdot 30m \cdot 10m \cdot \sin (60°))}{2 \cdot 20m \cdot 30m})

Next Step Convert Units

∴

∠γ = a \sin (\frac{1960m² - (2 \cdot 20m \cdot 10m \cdot \sin (0.7854rad)) - (2 \cdot 30m \cdot 10m \cdot \sin (1.0472rad))}{2 \cdot 20m \cdot 30m})

Next Step Prepare to Evaluate

∴

∠γ = a \sin (\frac{1960 - (2 \cdot 20 \cdot 10 \cdot \sin (0.7854)) - (2 \cdot 30 \cdot 10 \cdot \sin (1.0472))}{2 \cdot 20 \cdot 30})

Next Step Evaluate

∴

∠γ = 1.30399204093725rad

Next Step Convert to Output's Unit

∴

∠γ = 74.7132404643688°

LAST Step Rounding Answer

∴

∠γ = 74.7132°

Angle Gamma of Parallelepiped Formula Elements

Variables

Functions

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.

Symbol: ∠γ

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle Gamma of Parallelepiped

Total Surface Area of Parallelepiped

Total Surface Area of Parallelepiped is the total quantity of plane enclosed by the entire surface of the Parallelepiped.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Parallelepiped

Side B of Parallelepiped

Side B of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.

Symbol: S_b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side B of Parallelepiped

Side C of Parallelepiped

Side C of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.

Symbol: S_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side C of Parallelepiped

Angle Alpha of Parallelepiped

Angle Alpha of Parallelepiped is the angle formed by side B and side C at any of the two sharp tips of the Parallelepiped.

Symbol: ∠α

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle Alpha of Parallelepiped

Side A of Parallelepiped

Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.

Symbol: S_a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side A of Parallelepiped

Angle Beta of Parallelepiped

Angle Beta of Parallelepiped is the angle formed by side A and side C at any of the two sharp tips of the Parallelepiped.

Symbol: ∠β

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle Beta of Parallelepiped

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

asin

The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio.

Syntax: asin(Number)

Other formulas in Angle of Parallelepiped category

Go Angle Alpha of Parallelepiped

∠α = a \sin (\frac{TSA - (2 \cdot S a \cdot S b \cdot \sin (∠γ)) - (2 \cdot S a \cdot S c \cdot \sin (∠β))}{2 \cdot S c \cdot S b})

Go Angle Beta of Parallelepiped

∠β = a \sin (\frac{TSA - (2 \cdot S a \cdot S b \cdot \sin (∠γ)) - (2 \cdot S b \cdot S c \cdot \sin (∠α))}{2 \cdot S a \cdot S c})

How to Evaluate Angle Gamma of Parallelepiped?

Angle Gamma of Parallelepiped evaluator uses Angle Gamma of Parallelepiped = asin((Total Surface Area of Parallelepiped-(2*Side B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))-(2*Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped)))/(2*Side B of Parallelepiped*Side A of Parallelepiped)) to evaluate the Angle Gamma of Parallelepiped, Angle Gamma of Parallelepiped formula is defined as the angle formed by side A and side B at any of the two sharp tips of the Parallelepiped. Angle Gamma of Parallelepiped is denoted by ∠γ symbol.

How to evaluate Angle Gamma of Parallelepiped using this online evaluator? To use this online evaluator for Angle Gamma of Parallelepiped, enter Total Surface Area of Parallelepiped (TSA), Side B of Parallelepiped (S_b), Side C of Parallelepiped (S_c), Angle Alpha of Parallelepiped (∠α), Side A of Parallelepiped (S_a) & Angle Beta of Parallelepiped (∠β) and hit the calculate button.

FAQs on Angle Gamma of Parallelepiped

What is the formula to find Angle Gamma of Parallelepiped?

The formula of Angle Gamma of Parallelepiped is expressed as Angle Gamma of Parallelepiped = asin((Total Surface Area of Parallelepiped-(2*Side B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))-(2*Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped)))/(2*Side B of Parallelepiped*Side A of Parallelepiped)). Here is an example- 4280.753 = asin((1960-(2*20*10*sin(0.785398163397301))-(2*30*10*sin(1.0471975511964)))/(2*20*30)).

How to calculate Angle Gamma of Parallelepiped?

With Total Surface Area of Parallelepiped (TSA), Side B of Parallelepiped (S_b), Side C of Parallelepiped (S_c), Angle Alpha of Parallelepiped (∠α), Side A of Parallelepiped (S_a) & Angle Beta of Parallelepiped (∠β) we can find Angle Gamma of Parallelepiped using the formula - Angle Gamma of Parallelepiped = asin((Total Surface Area of Parallelepiped-(2*Side B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))-(2*Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped)))/(2*Side B of Parallelepiped*Side A of Parallelepiped)). This formula also uses Sine (sin), Inverse Sine (asin) function(s).

Can the Angle Gamma of Parallelepiped be negative?

No, the Angle Gamma of Parallelepiped, measured in Angle cannot be negative.

Which unit is used to measure Angle Gamma of Parallelepiped?

Angle Gamma of Parallelepiped is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle Gamma of Parallelepiped can be measured.

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Angle Gamma of Parallelepiped Formula

Angle Gamma of Parallelepiped Example

Angle Gamma of Parallelepiped Solution

Angle Gamma of Parallelepiped Formula Elements

Other formulas in Angle of Parallelepiped category

How to Evaluate Angle Gamma of Parallelepiped?

FAQs on Angle Gamma of Parallelepiped

Variable Name