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Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals Formula

GoLong Diagonal of Parallelogram given Sides and Acute Angle between Sides Formula

GoLong Diagonal of Parallelogram given Sides and Obtuse Angle between sides Formula

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

d Long = \frac{2 \cdot A}{d Short \cdot \sin (∠ d(Acute))}

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

Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals Example

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Here is how the Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals equation looks like with Values.

Here is how the Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals equation looks like with Units.

Here is how the Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals equation looks like.

17.4054 = \frac{2 \cdot 60}{9 \cdot \sin (50)}

17.4054m = \frac{2 \cdot 60m²}{9m \cdot \sin (50°)}

17.4054 = \frac{2 \cdot 60}{9 \cdot \sin (50)}

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Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals Solution

Follow our step by step solution on how to calculate Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals?

FIRST Step Consider the formula

d Long = \frac{2 \cdot A}{d Short \cdot \sin (∠ d(Acute))}

Next Step Substitute values of Variables

∴

d Long = \frac{2 \cdot 60m²}{9m \cdot \sin (50°)}

Next Step Convert Units

∴

d Long = \frac{2 \cdot 60m²}{9m \cdot \sin (0.8727rad)}

Next Step Prepare to Evaluate

∴

d Long = \frac{2 \cdot 60}{9 \cdot \sin (0.8727)}

Next Step Evaluate

∴

d Long = 17.4054305244328m

LAST Step Rounding Answer

∴

d Long = 17.4054m

Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals Formula Elements

Variables

Functions

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

Area of Parallelogram

Area of Parallelogram is the total quantity of plane enclosed by the boundary of the Parallelogram.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area 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

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)

Other Formulas to find Long Diagonal of Parallelogram

Go Long Diagonal of Parallelogram given Sides and Acute Angle between Sides

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

Go Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides

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

Go Long Diagonal of Parallelogram

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

How to Evaluate Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals?

Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals evaluator uses Long Diagonal of Parallelogram = (2*Area of Parallelogram)/(Short Diagonal of Parallelogram*sin(Acute Angle between Diagonals of Parallelogram)) to evaluate the Long Diagonal of Parallelogram, Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals formula is defined as the length of the line joining the pair of acute angle corners of a Parallelogram, and calculated using area, short diagonal and acute angle between diagonal of the Parallelogram. Long Diagonal of Parallelogram is denoted by d_Long symbol.

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

FAQs on Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals

What is the formula to find Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals?

The formula of Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals is expressed as Long Diagonal of Parallelogram = (2*Area of Parallelogram)/(Short Diagonal of Parallelogram*sin(Acute Angle between Diagonals of Parallelogram)). Here is an example- 17.40543 = (2*60)/(9*sin(0.872664625997001)).

How to calculate Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals?

With Area of Parallelogram (A), Short Diagonal of Parallelogram (d_Short) & Acute Angle between Diagonals of Parallelogram (∠_d(Acute)) we can find Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals using the formula - Long Diagonal of Parallelogram = (2*Area of Parallelogram)/(Short Diagonal of Parallelogram*sin(Acute Angle between Diagonals of Parallelogram)). This formula also uses Sine function(s).

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

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

Long Diagonal of Parallelogram=sqrt(Long Edge of Parallelogram^2+Short Edge of Parallelogram^2+(2*Long Edge of Parallelogram*Short Edge of Parallelogram*cos(Acute Angle of Parallelogram)))
Long Diagonal of Parallelogram=sqrt(Long Edge of Parallelogram^2+Short Edge of Parallelogram^2-(2*Long Edge of Parallelogram*Short Edge of Parallelogram*cos(Obtuse Angle of Parallelogram)))
Long Diagonal of Parallelogram=sqrt((2*Long Edge of Parallelogram^2)+(2*Short Edge of Parallelogram^2)-Short Diagonal of Parallelogram^2)

Can the Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals be negative?

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

Which unit is used to measure Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals?

Long Diagonal of Parallelogram given Area, Short Diagonal 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 Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals can be measured.

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Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals Formula

​GoLong Diagonal of Parallelogram given Sides and Acute Angle between Sides Formula

​GoLong Diagonal of Parallelogram given Sides and Obtuse Angle between sides Formula

Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals Example

Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals Solution

Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals Formula Elements

Other Formulas to find Long Diagonal of Parallelogram

How to Evaluate Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals?

FAQs on Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals

Variable Name

GoLong Diagonal of Parallelogram given Sides and Acute Angle between Sides Formula

GoLong Diagonal of Parallelogram given Sides and Obtuse Angle between sides Formula