Angle Beta of Parallelepiped Calculator

✖Total Surface Area of Parallelepiped is the total quantity of plane enclosed by the entire surface of the Parallelepiped.ⓘ Total Surface Area of Parallelepiped [TSA]			+10% -10%
✖Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.ⓘ Side A of Parallelepiped [S_a]			+10% -10%
✖Side B of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.ⓘ Side B of Parallelepiped [S_b]			+10% -10%
✖Angle Gamma of Parallelepiped is the angle formed by side A and side B at any of the two sharp tips of the Parallelepiped.ⓘ Angle Gamma of Parallelepiped [∠γ]			+10% -10%
✖Side C of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.ⓘ Side C of Parallelepiped [S_c]			+10% -10%
✖Angle Alpha of Parallelepiped is the angle formed by side B and side C at any of the two sharp tips of the Parallelepiped.ⓘ Angle Alpha of Parallelepiped [∠α]			+10% -10%

✖Angle Beta of Parallelepiped is the angle formed by side A and side C at any of the two sharp tips of the Parallelepiped.ⓘ Angle Beta of Parallelepiped [∠β]

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Formula

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Angle Beta of Parallelepiped

Formula

`"∠β" = asin(("TSA"-(2*"S"_{"a"}*"S"_{"b"}*sin("∠γ"))-(2*"S"_{"b"}*"S"_{"c"}*sin("∠α")))/(2*"S"_{"a"}*"S"_{"c"}))`

Example

`"59.7017°"=asin(("1960m²"-(2*"30m"*"20m"*sin("75°"))-(2*"20m"*"10m"*sin("45°")))/(2*"30m"*"10m"))`

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Angle Beta of Parallelepiped Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle Beta of Parallelepiped = asin((Total Surface Area of Parallelepiped-(2*Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma 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))
∠β = asin((TSA-(2*S_a*S_b*sin(∠γ))-(2*S_b*S_c*sin(∠α)))/(2*S_a*S_c))
This formula uses 2 Functions, 7 Variables

Functions Used

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., 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., asin(Number)

Variables Used

Angle Beta of Parallelepiped - (Measured in Radian) - Angle Beta of Parallelepiped is the angle formed by side A and side C at any of the two sharp tips of the Parallelepiped.
Total Surface Area of Parallelepiped - (Measured in Square Meter) - Total Surface Area of Parallelepiped is the total quantity of plane enclosed by the entire surface of the Parallelepiped.
Side A of Parallelepiped - (Measured in Meter) - Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.
Side B of Parallelepiped - (Measured in Meter) - Side B of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.
Angle Gamma of Parallelepiped - (Measured in Radian) - Angle Gamma of Parallelepiped is the angle formed by side A and side B at any of the two sharp tips of the Parallelepiped.
Side C of Parallelepiped - (Measured in Meter) - Side C of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.
Angle Alpha of Parallelepiped - (Measured in Radian) - Angle Alpha of Parallelepiped is the angle formed by side B and side C at any of the two sharp tips of the Parallelepiped.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Parallelepiped: 1960 Square Meter --> 1960 Square Meter No Conversion Required
Side A of Parallelepiped: 30 Meter --> 30 Meter No Conversion Required
Side B of Parallelepiped: 20 Meter --> 20 Meter No Conversion Required
Angle Gamma of Parallelepiped: 75 Degree --> 1.3089969389955 Radian (Check conversion here)
Side C of Parallelepiped: 10 Meter --> 10 Meter No Conversion Required
Angle Alpha of Parallelepiped: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠β = asin((TSA-(2*S_a*S_b*sin(∠γ))-(2*S_b*S_c*sin(∠α)))/(2*S_a*S_c)) --> asin((1960-(2*30*20*sin(1.3089969389955))-(2*20*10*sin(0.785398163397301)))/(2*30*10))

Evaluating ... ...

∠β = 1.04199118138206

STEP 3: Convert Result to Output's Unit

1.04199118138206 Radian -->59.7016969830541 Degree (Check conversion here)

FINAL ANSWER

59.7016969830541 ≈ 59.7017 Degree <-- Angle Beta of Parallelepiped

(Calculation completed in 00.004 seconds)

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< 3 Angle of Parallelepiped Calculators

Angle Alpha of Parallelepiped

Go 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))

Angle Gamma of Parallelepiped

Go 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))

Angle Beta of Parallelepiped

Go Angle Beta of Parallelepiped = asin((Total Surface Area of Parallelepiped-(2*Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma 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))

< 3 Angle of Parallelepiped Calculators

Angle Alpha of Parallelepiped

Angle Gamma of Parallelepiped

Angle Beta of Parallelepiped

Angle Beta of Parallelepiped Formula

What is a Parallelepiped?

A Parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square. In Euclidean geometry, the four concepts—parallelepiped and cube in three dimensions, parallelogram and square in two dimensions—are defined, but in the context of a more general affine geometry, in which angles are not differentiated, only parallelograms and parallelepipeds exist.

How to Calculate Angle Beta of Parallelepiped?

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

How to calculate Angle Beta of Parallelepiped using this online calculator? To use this online calculator for Angle Beta 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 Alpha of Parallelepiped (∠α) and hit the calculate button. Here is how the Angle Beta of Parallelepiped calculation can be explained with given input values -> 3420.655 = asin((1960-(2*30*20*sin(1.3089969389955))-(2*20*10*sin(0.785398163397301)))/(2*30*10)).

FAQ

What is Angle Beta of Parallelepiped?

Angle Beta of Parallelepiped formula is defined as the angle formed by side A and side C at any of the two sharp tips of the Parallelepiped and is represented as ∠β = asin((TSA-(2*S_a*S_b*sin(∠γ))-(2*S_b*S_c*sin(∠α)))/(2*S_a*S_c)) or Angle Beta of Parallelepiped = asin((Total Surface Area of Parallelepiped-(2*Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma 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)). Total Surface Area of Parallelepiped is the total quantity of plane enclosed by the entire surface of the Parallelepiped, Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped, Side B of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the 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, Side C of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the 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.

How to calculate Angle Beta of Parallelepiped?

Angle Beta of Parallelepiped formula is defined as the angle formed by side A and side C at any of the two sharp tips of the Parallelepiped is calculated using Angle Beta of Parallelepiped = asin((Total Surface Area of Parallelepiped-(2*Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma 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)). To calculate Angle Beta of Parallelepiped, you need 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 Alpha of Parallelepiped (∠α). With our tool, you need to enter the respective value for Total Surface Area of Parallelepiped, Side A of Parallelepiped, Side B of Parallelepiped, Angle Gamma of Parallelepiped, Side C of Parallelepiped & Angle Alpha of Parallelepiped and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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