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Diagonal of Parallelogram given sides and angle between sides Solution

STEP 0: Pre-Calculation Summary
Formula Used
diagonal = sqrt((Side C)^2+(Side D)^2+2*Side C*Side D*cos(Theta))
d = sqrt((Sc)^2+(Sd)^2+2*Sc*Sd*cos(ϑ))
This formula uses 2 Functions, 3 Variables
Functions Used
cos - Trigonometric cosine function, cos(Angle)
sqrt - Squre root function, sqrt(Number)
Variables Used
Side C - Side C is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
Side D - Side D is a straight line bounding a geometric figure. (Measured in Meter)
Theta - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint. (Measured in Degree)
STEP 1: Convert Input(s) to Base Unit
Side C: 4 Meter --> 4 Meter No Conversion Required
Side D: 5 Meter --> 5 Meter No Conversion Required
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d = sqrt((Sc)^2+(Sd)^2+2*Sc*Sd*cos(ϑ)) --> sqrt((4)^2+(5)^2+2*4*5*cos(0.5235987755982))
Evaluating ... ...
d = 8.69718438067042
STEP 3: Convert Result to Output's Unit
8.69718438067042 Meter --> No Conversion Required
FINAL ANSWER
8.69718438067042 Meter <-- Diagonal
(Calculation completed in 00.017 seconds)

8 Diagonal of Parallelogram Calculators

Short Diagonal of Parallelogram given obtuse angle
short_diagonal = sqrt(Side C^2+Side D^2+2*Side C*Side D*cos(Obtuse Angle)) Go
Short Diagonal of Parallelogram given acute angle
short_diagonal = sqrt(Side C^2+Side D^2-(2*Side C*Side D*cos(Acute Angle))) Go
Long Diagonal of Parallelogram given obtuse angle
long_diagonal = sqrt(Side C^2+Side D^2-2*Side C*Side D*cos(Obtuse Angle)) Go
Long Diagonal of Parallelogram given acute angle
long_diagonal = sqrt(Side C^2+Side D^2+2*Side C*Side D*cos(Acute Angle)) Go
Diagonal of Parallelogram given sides and angle between sides
diagonal = sqrt((Side C)^2+(Side D)^2+2*Side C*Side D*cos(Theta)) Go
Long Diagonal of Parallelogram given area, short diagonal and angles between diagonals
long_diagonal = (2*Area)/(Short diagonal*sin(Angle Between Two Diagonals)) Go
Short Diagonal of Parallelogram given area, long diagonal and angle between diagonals
short_diagonal = (2*Area)/(Long diagonal*sin(Angle Between Two Diagonals)) Go
Long Diagonal of Parallelogram given short diagonal
long_diagonal = sqrt(2*Side C^2+2*Side D^2-Short diagonal^2) Go

Diagonal of Parallelogram given sides and angle between sides Formula

diagonal = sqrt((Side C)^2+(Side D)^2+2*Side C*Side D*cos(Theta))
d = sqrt((Sc)^2+(Sd)^2+2*Sc*Sd*cos(ϑ))

What is parallelogram?

A parallelogram is a special type of quadrilateral that has equal and parallel opposite sides. The opposite sides of a parallelogram are parallel to each other.

How to Calculate Diagonal of Parallelogram given sides and angle between sides?

Diagonal of Parallelogram given sides and angle between sides calculator uses diagonal = sqrt((Side C)^2+(Side D)^2+2*Side C*Side D*cos(Theta)) to calculate the Diagonal, Diagonal of parallelogram given sides and angle between sides is any segment that connects two vertices of a parallelogram opposite angles. Diagonal and is denoted by d symbol.

How to calculate Diagonal of Parallelogram given sides and angle between sides using this online calculator? To use this online calculator for Diagonal of Parallelogram given sides and angle between sides, enter Side C (Sc), Side D (Sd) & Theta (ϑ) and hit the calculate button. Here is how the Diagonal of Parallelogram given sides and angle between sides calculation can be explained with given input values -> 8.697184 = sqrt((4)^2+(5)^2+2*4*5*cos(0.5235987755982)).

FAQ

What is Diagonal of Parallelogram given sides and angle between sides?
Diagonal of parallelogram given sides and angle between sides is any segment that connects two vertices of a parallelogram opposite angles and is represented as d = sqrt((Sc)^2+(Sd)^2+2*Sc*Sd*cos(ϑ)) or diagonal = sqrt((Side C)^2+(Side D)^2+2*Side C*Side D*cos(Theta)). Side C is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back, Side D is a straight line bounding a geometric figure & Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
How to calculate Diagonal of Parallelogram given sides and angle between sides?
Diagonal of parallelogram given sides and angle between sides is any segment that connects two vertices of a parallelogram opposite angles is calculated using diagonal = sqrt((Side C)^2+(Side D)^2+2*Side C*Side D*cos(Theta)). To calculate Diagonal of Parallelogram given sides and angle between sides, you need Side C (Sc), Side D (Sd) & Theta (ϑ). With our tool, you need to enter the respective value for Side C, Side D & Theta and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Diagonal?
In this formula, Diagonal uses Side C, Side D & Theta. We can use 8 other way(s) to calculate the same, which is/are as follows -
  • diagonal = sqrt((Side C)^2+(Side D)^2+2*Side C*Side D*cos(Theta))
  • long_diagonal = (2*Area)/(Short diagonal*sin(Angle Between Two Diagonals))
  • short_diagonal = (2*Area)/(Long diagonal*sin(Angle Between Two Diagonals))
  • long_diagonal = sqrt(Side C^2+Side D^2+2*Side C*Side D*cos(Acute Angle))
  • long_diagonal = sqrt(Side C^2+Side D^2-2*Side C*Side D*cos(Obtuse Angle))
  • short_diagonal = sqrt(Side C^2+Side D^2-(2*Side C*Side D*cos(Acute Angle)))
  • short_diagonal = sqrt(Side C^2+Side D^2+2*Side C*Side D*cos(Obtuse Angle))
  • long_diagonal = sqrt(2*Side C^2+2*Side D^2-Short diagonal^2)
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