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Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals Formula

GoLong Edge of Parallelogram given Diagonals and Short Edge Formula

GoLong Edge of Parallelogram given Height to Short Edge and Acute Angle between Sides Formula

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Long Edge of Parallelogram is the length of the longest pair of parallel sides in a Parallelogram. Check FAQs

e Long = \frac{1}{2} \cdot \sqrt{{d Long}^{2} + {d Short}^{2} + (2 \cdot d Long \cdot d Short \cdot \cos (∠ d(Acute)))}

e_Long - Long Edge of Parallelogram?d_Long - Long Diagonal of Parallelogram?d_Short - Short Diagonal of Parallelogram?∠_d(Acute) - Acute Angle between Diagonals of Parallelogram?

Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals Example

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Here is how the Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals equation looks like with Values.

Here is how the Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals equation looks like with Units.

Here is how the Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals equation looks like.

12.3821 = \frac{1}{2} \cdot \sqrt{18^{2} + 9^{2} + (2 \cdot 18 \cdot 9 \cdot \cos (50))}

12.3821m = \frac{1}{2} \cdot \sqrt{{18m}^{2} + {9m}^{2} + (2 \cdot 18m \cdot 9m \cdot \cos (50°))}

12.3821 = \frac{1}{2} \cdot \sqrt{18^{2} + 9^{2} + (2 \cdot 18 \cdot 9 \cdot \cos (50))}

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Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals Solution

Follow our step by step solution on how to calculate Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals?

FIRST Step Consider the formula

e Long = \frac{1}{2} \cdot \sqrt{{d Long}^{2} + {d Short}^{2} + (2 \cdot d Long \cdot d Short \cdot \cos (∠ d(Acute)))}

Next Step Substitute values of Variables

∴

e Long = \frac{1}{2} \cdot \sqrt{{18m}^{2} + {9m}^{2} + (2 \cdot 18m \cdot 9m \cdot \cos (50°))}

Next Step Convert Units

∴

e Long = \frac{1}{2} \cdot \sqrt{{18m}^{2} + {9m}^{2} + (2 \cdot 18m \cdot 9m \cdot \cos (0.8727rad))}

Next Step Prepare to Evaluate

∴

e Long = \frac{1}{2} \cdot \sqrt{18^{2} + 9^{2} + (2 \cdot 18 \cdot 9 \cdot \cos (0.8727))}

Next Step Evaluate

∴

e Long = 12.3820756089042m

LAST Step Rounding Answer

∴

e Long = 12.3821m

Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals Formula Elements

Variables

Functions

Long Edge of Parallelogram

Long Edge of Parallelogram is the length of the longest pair of parallel sides in a Parallelogram.

Symbol: e_Long

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Edge of Parallelogram

Long Diagonal of Parallelogram

Long Diagonal of Parallelogram is the length of the line joining the pair of acute angle corners of a Parallelogram.

Symbol: d_Long

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Diagonal of Parallelogram

Short Diagonal of Parallelogram

Short Diagonal of Parallelogram is the length of the line joining the pair of obtuse angle corners of a Parallelogram.

Symbol: d_Short

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Diagonal of Parallelogram

Acute Angle between Diagonals of Parallelogram

Acute Angle between Diagonals of Parallelogram is the angle made by the diagonals of the Parallelogram which is less than 90 degree.

Symbol: ∠_d(Acute)

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Acute Angle between Diagonals of Parallelogram

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Long Edge of Parallelogram

Go Long Edge of Parallelogram given Diagonals and Short Edge

e Long = \sqrt{\frac{{d Long}^{2} + {d Short}^{2} - (2 \cdot {e Short}^{2})}{2}}

Go Long Edge of Parallelogram given Height to Short Edge and Acute Angle between Sides

e Long = \frac{h Short}{\sin (∠ Acute)}

Go Long Edge of Parallelogram

e Long = \frac{A}{h Long}

Go Long Edge of Parallelogram given Diagonals and Obtuse Angle between Diagonals

e Long = \frac{1}{2} \cdot \sqrt{{d Long}^{2} + {d Short}^{2} - (2 \cdot d Long \cdot d Short \cdot \cos (∠ d(Obtuse)))}

How to Evaluate Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals?

Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals evaluator uses Long Edge of Parallelogram = 1/2*sqrt(Long Diagonal of Parallelogram^2+Short Diagonal of Parallelogram^2+(2*Long Diagonal of Parallelogram*Short Diagonal of Parallelogram*cos(Acute Angle between Diagonals of Parallelogram))) to evaluate the Long Edge of Parallelogram, Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals formula is defined as the length of the longest pair of parallel sides in a Parallelogram, and calculated using diagonals and acute angle between diagonals of the Parallelogram. Long Edge of Parallelogram is denoted by e_Long symbol.

How to evaluate Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals using this online evaluator? To use this online evaluator for Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals, enter Long Diagonal of Parallelogram (d_Long), Short Diagonal of Parallelogram (d_Short) & Acute Angle between Diagonals of Parallelogram (∠_d(Acute)) and hit the calculate button.

FAQs on Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals

What is the formula to find Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals?

The formula of Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals is expressed as Long Edge of Parallelogram = 1/2*sqrt(Long Diagonal of Parallelogram^2+Short Diagonal of Parallelogram^2+(2*Long Diagonal of Parallelogram*Short Diagonal of Parallelogram*cos(Acute Angle between Diagonals of Parallelogram))). Here is an example- 12.38208 = 1/2*sqrt(18^2+9^2+(2*18*9*cos(0.872664625997001))).

How to calculate Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals?

With Long Diagonal of Parallelogram (d_Long), Short Diagonal of Parallelogram (d_Short) & Acute Angle between Diagonals of Parallelogram (∠_d(Acute)) we can find Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals using the formula - Long Edge of Parallelogram = 1/2*sqrt(Long Diagonal of Parallelogram^2+Short Diagonal of Parallelogram^2+(2*Long Diagonal of Parallelogram*Short Diagonal of Parallelogram*cos(Acute Angle between Diagonals of Parallelogram))). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Long Edge of Parallelogram?

Here are the different ways to Calculate Long Edge of Parallelogram-

Long Edge of Parallelogram=sqrt((Long Diagonal of Parallelogram^2+Short Diagonal of Parallelogram^2-(2*Short Edge of Parallelogram^2))/2)
Long Edge of Parallelogram=Height to Short Edge of Parallelogram/(sin(Acute Angle of Parallelogram))
Long Edge of Parallelogram=Area of Parallelogram/Height to Long Edge of Parallelogram

Can the Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals be negative?

No, the Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals, measured in Length cannot be negative.

Which unit is used to measure Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals?

Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals can be measured.

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Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals Formula

​GoLong Edge of Parallelogram given Diagonals and Short Edge Formula

​GoLong Edge of Parallelogram given Height to Short Edge and Acute Angle between Sides Formula

Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals Example

Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals Solution

Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals Formula Elements

Other Formulas to find Long Edge of Parallelogram

How to Evaluate Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals?

FAQs on Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals

Variable Name

GoLong Edge of Parallelogram given Diagonals and Short Edge Formula

GoLong Edge of Parallelogram given Height to Short Edge and Acute Angle between Sides Formula