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Angle Alpha of Parallelepiped Formula

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

∠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})

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

Angle Alpha of Parallelepiped Example

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

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

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

44.6831 = a \sin (\frac{1960 - (2 \cdot 30 \cdot 20 \cdot \sin (75)) - (2 \cdot 30 \cdot 10 \cdot \sin (60))}{2 \cdot 10 \cdot 20})

44.6831° = a \sin (\frac{1960m² - (2 \cdot 30m \cdot 20m \cdot \sin (75°)) - (2 \cdot 30m \cdot 10m \cdot \sin (60°))}{2 \cdot 10m \cdot 20m})

44.6831 = a \sin (\frac{1960 - (2 \cdot 30 \cdot 20 \cdot \sin (75)) - (2 \cdot 30 \cdot 10 \cdot \sin (60))}{2 \cdot 10 \cdot 20})

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Home » Math » Geometry » 3D Geometry » Angle Alpha of Parallelepiped

Angle Alpha of Parallelepiped Solution

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

FIRST Step Consider the formula

∠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})

Next Step Substitute values of Variables

∴

∠α = a \sin (\frac{1960m² - (2 \cdot 30m \cdot 20m \cdot \sin (75°)) - (2 \cdot 30m \cdot 10m \cdot \sin (60°))}{2 \cdot 10m \cdot 20m})

Next Step Convert Units

∴

∠α = a \sin (\frac{1960m² - (2 \cdot 30m \cdot 20m \cdot \sin (1.309rad)) - (2 \cdot 30m \cdot 10m \cdot \sin (1.0472rad))}{2 \cdot 10m \cdot 20m})

Next Step Prepare to Evaluate

∴

∠α = a \sin (\frac{1960 - (2 \cdot 30 \cdot 20 \cdot \sin (1.309)) - (2 \cdot 30 \cdot 10 \cdot \sin (1.0472))}{2 \cdot 10 \cdot 20})

Next Step Evaluate

∴

∠α = 0.779866372687863rad

Next Step Convert to Output's Unit

∴

∠α = 44.6830517391995°

LAST Step Rounding Answer

∴

∠α = 44.6831°

Angle Alpha of Parallelepiped Formula Elements

Variables

Functions

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.

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.

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.

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.

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.

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.

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.

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)

Credits

Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has created this Formula and 2000+ more formulas!

Verified by

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Formula and 1700+ more formulas!

Other formulas in Angle of Parallelepiped category

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})

Go Angle Gamma of Parallelepiped

∠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})

How to Evaluate Angle Alpha of Parallelepiped?

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

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

FAQs on Angle Alpha of Parallelepiped

What is the formula to find Angle Alpha of Parallelepiped?

The formula of Angle Alpha of Parallelepiped is expressed as Angle Alpha of Parallelepiped = asin((Total Surface Area of Parallelepiped-(2*Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))-(2*Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped)))/(2*Side C of Parallelepiped*Side B of Parallelepiped)). Here is an example- 2560.15 = asin((1960-(2*30*20*sin(1.3089969389955))-(2*30*10*sin(1.0471975511964)))/(2*10*20)).

How to calculate Angle Alpha of Parallelepiped?

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

Can the Angle Alpha of Parallelepiped be negative?

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

Which unit is used to measure Angle Alpha of Parallelepiped?

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

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Angle Alpha of Parallelepiped Formula

Angle Alpha of Parallelepiped Example

Angle Alpha of Parallelepiped Solution

Angle Alpha of Parallelepiped Formula Elements

Credits

Other formulas in Angle of Parallelepiped category

How to Evaluate Angle Alpha of Parallelepiped?

FAQs on Angle Alpha of Parallelepiped

Variable Name