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

GoLong 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

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

d_Long - Long Diagonal of Parallelogram?e_Long - Long Edge of Parallelogram?e_Short - Short Edge of Parallelogram?∠_Obtuse - Obtuse Angle of Parallelogram?

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

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Here is how the Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides equation looks like with Values.

Here is how the Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides equation looks like with Units.

Here is how the Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides equation looks like.

17.6577 = \sqrt{12^{2} + 7^{2} - (2 \cdot 12 \cdot 7 \cdot \cos (135))}

17.6577m = \sqrt{{12m}^{2} + {7m}^{2} - (2 \cdot 12m \cdot 7m \cdot \cos (135°))}

17.6577 = \sqrt{12^{2} + 7^{2} - (2 \cdot 12 \cdot 7 \cdot \cos (135))}

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

Follow our step by step solution on how to calculate Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d Long = \sqrt{{12m}^{2} + {7m}^{2} - (2 \cdot 12m \cdot 7m \cdot \cos (135°))}

Next Step Convert Units

∴

d Long = \sqrt{{12m}^{2} + {7m}^{2} - (2 \cdot 12m \cdot 7m \cdot \cos (2.3562rad))}

Next Step Prepare to Evaluate

∴

d Long = \sqrt{12^{2} + 7^{2} - (2 \cdot 12 \cdot 7 \cdot \cos (2.3562))}

Next Step Evaluate

∴

d Long = 17.6576878225686m

LAST Step Rounding Answer

∴

d Long = 17.6577m

Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides 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

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

Short Edge of Parallelogram

Short Edge of Parallelogram is the length of the shortest pair of parallel edges in a Parallelogram.

Symbol: e_Short

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Edge of Parallelogram

Obtuse Angle of Parallelogram

Obtuse Angle of Parallelogram is the measure of pair of opposite angles which are greater than 90 degree in a Parallelogram.

Symbol: ∠_Obtuse

Measurement: AngleUnit: °

Note: Value should be between 90 to 180.

Formulas to find Obtuse Angle 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 Diagonal of Parallelogram

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

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

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

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

How to Evaluate Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides?

Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides evaluator uses 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))) to evaluate the Long Diagonal of Parallelogram, Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides formula is defined as the length of the line joining the pair of acute angle corners of a Parallelogram, calculated using sides and obtuse angle between sides. Long Diagonal of Parallelogram is denoted by d_Long symbol.

How to evaluate Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides using this online evaluator? To use this online evaluator for Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides, enter Long Edge of Parallelogram (e_Long), Short Edge of Parallelogram (e_Short) & Obtuse Angle of Parallelogram (∠_Obtuse) and hit the calculate button.

FAQs on Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides

What is the formula to find Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides?

The formula of Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides is expressed as 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))). Here is an example- 17.65769 = sqrt(12^2+7^2-(2*12*7*cos(2.3561944901919))).

How to calculate Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides?

With Long Edge of Parallelogram (e_Long), Short Edge of Parallelogram (e_Short) & Obtuse Angle of Parallelogram (∠_Obtuse) we can find Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides using the formula - 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))). This formula also uses Cosine (cos), Square Root (sqrt) 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=(2*Area of Parallelogram)/(Short Diagonal of Parallelogram*sin(Acute Angle between Diagonals 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((2*Long Edge of Parallelogram^2)+(2*Short Edge of Parallelogram^2)-Short Diagonal of Parallelogram^2)

Can the Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides be negative?

No, the Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides, measured in Length cannot be negative.

Which unit is used to measure Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides?

Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides 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 Sides and Obtuse Angle between sides can be measured.

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

​GoLong 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

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

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

Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides Formula Elements

Other Formulas to find Long Diagonal of Parallelogram

How to Evaluate Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides?

FAQs on Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides

Variable Name

GoLong 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