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

✖Long Diagonal of Parallelogram is the length of the line joining the pair of acute angle corners of a Parallelogram.ⓘ Long Diagonal of Parallelogram [d_Long]			+10% -10%
✖Short Diagonal of Parallelogram is the length of the line joining the pair of obtuse angle corners of a Parallelogram.ⓘ Short Diagonal of Parallelogram [d_Short]			+10% -10%
✖Obtuse Angle between Diagonals of Parallelogram is the angle made by the diagonals of the Parallelogram which is greater than 90 degree.ⓘ Obtuse Angle between Diagonals of Parallelogram [∠_d(Obtuse)]			+10% -10%

✖Long Edge of Parallelogram is the length of the longest pair of parallel sides in a Parallelogram.ⓘ Long Edge of Parallelogram given Diagonals and Obtuse Angle between Diagonals [e_Long]

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

STEP 0: Pre-Calculation Summary

Formula Used

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(Obtuse Angle between Diagonals of Parallelogram)))
e_Long = 1/2*sqrt(d_Long^2+d_Short^2-(2*d_Long*d_Short*cos(∠_d(Obtuse))))
This formula uses 2 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., sqrt(Number)

Variables Used

Long Edge of Parallelogram - (Measured in Meter) - Long Edge of Parallelogram is the length of the longest pair of parallel sides in a Parallelogram.
Long Diagonal of Parallelogram - (Measured in Meter) - Long Diagonal of Parallelogram is the length of the line joining the pair of acute angle corners of a Parallelogram.
Short Diagonal of Parallelogram - (Measured in Meter) - Short Diagonal of Parallelogram is the length of the line joining the pair of obtuse angle corners of a Parallelogram.
Obtuse Angle between Diagonals of Parallelogram - (Measured in Radian) - Obtuse Angle between Diagonals of Parallelogram is the angle made by the diagonals of the Parallelogram which is greater than 90 degree.

STEP 1: Convert Input(s) to Base Unit

Long Diagonal of Parallelogram: 18 Meter --> 18 Meter No Conversion Required
Short Diagonal of Parallelogram: 9 Meter --> 9 Meter No Conversion Required
Obtuse Angle between Diagonals of Parallelogram: 130 Degree --> 2.2689280275922 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e_Long = 1/2*sqrt(d_Long^2+d_Short^2-(2*d_Long*d_Short*cos(∠_d(Obtuse)))) --> 1/2*sqrt(18^2+9^2-(2*18*9*cos(2.2689280275922)))

Evaluating ... ...

e_Long = 12.3820756089027

STEP 3: Convert Result to Output's Unit

12.3820756089027 Meter --> No Conversion Required

FINAL ANSWER

12.3820756089027 ≈ 12.38208 Meter <-- Long Edge of Parallelogram

(Calculation completed in 00.007 seconds)

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Vellore Institute of Technology (VIT), Bhopal

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< Long Edge of Parallelogram Calculators

Long Edge of Parallelogram given Diagonals and Acute Angle between Diagonals

LaTeX Go 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)))

Long Edge of Parallelogram given Diagonals and Short Edge

LaTeX Go 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 given Height to Short Edge and Acute Angle between Sides

LaTeX Go Long Edge of Parallelogram = Height to Short Edge of Parallelogram/(sin(Acute Angle of Parallelogram))

Long Edge of Parallelogram

LaTeX Go Long Edge of Parallelogram = Area of Parallelogram/Height to Long Edge of Parallelogram

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

LaTeX Go

What is a Parallelogram?

A Parallelogram is a special type of quadrilateral that has two pairs of opposite and parallel sides. Rectangles are a special type of Parallelogram. The angles of Parallelogram are also pairwise equal and opposite - one pair of equal and opposite acute angle and one pair of equal and opposite obtuse angle angle.

How to Calculate Long Edge of Parallelogram given Diagonals and Obtuse Angle between Diagonals?

Long Edge of Parallelogram given Diagonals and Obtuse Angle between Diagonals calculator 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(Obtuse Angle between Diagonals of Parallelogram))) to calculate the Long Edge of Parallelogram, Long Edge of Parallelogram given Diagonals and Obtuse Angle between Diagonals formula is defined as the length of the longest pair of parallel sides in a Parallelogram, and calculated using diagonals and obtuse angle between diagonals of the Parallelogram. Long Edge of Parallelogram is denoted by e_Long symbol.

How to calculate Long Edge of Parallelogram given Diagonals and Obtuse Angle between Diagonals using this online calculator? To use this online calculator for Long Edge of Parallelogram given Diagonals and Obtuse Angle between Diagonals, enter Long Diagonal of Parallelogram (d_Long), Short Diagonal of Parallelogram (d_Short) & Obtuse Angle between Diagonals of Parallelogram (∠_d(Obtuse)) and hit the calculate button. Here is how the Long Edge of Parallelogram given Diagonals and Obtuse Angle between Diagonals calculation can be explained with given input values -> 12.38208 = 1/2*sqrt(18^2+9^2-(2*18*9*cos(2.2689280275922))).

FAQ

What is Long Edge of Parallelogram given Diagonals and Obtuse Angle between Diagonals?

Long Edge of Parallelogram given Diagonals and Obtuse Angle between Diagonals formula is defined as the length of the longest pair of parallel sides in a Parallelogram, and calculated using diagonals and obtuse angle between diagonals of the Parallelogram and is represented as e_Long = 1/2*sqrt(d_Long^2+d_Short^2-(2*d_Long*d_Short*cos(∠_d(Obtuse)))) or 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(Obtuse Angle between Diagonals of Parallelogram))). Long Diagonal of Parallelogram is the length of the line joining the pair of acute angle corners of a Parallelogram, Short Diagonal of Parallelogram is the length of the line joining the pair of obtuse angle corners of a Parallelogram & Obtuse Angle between Diagonals of Parallelogram is the angle made by the diagonals of the Parallelogram which is greater than 90 degree.

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

Long Edge of Parallelogram given Diagonals and Obtuse Angle between Diagonals formula is defined as the length of the longest pair of parallel sides in a Parallelogram, and calculated using diagonals and obtuse angle between diagonals of the Parallelogram is calculated using 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(Obtuse Angle between Diagonals of Parallelogram))). To calculate Long Edge of Parallelogram given Diagonals and Obtuse Angle between Diagonals, you need Long Diagonal of Parallelogram (d_Long), Short Diagonal of Parallelogram (d_Short) & Obtuse Angle between Diagonals of Parallelogram (∠_d(Obtuse)). With our tool, you need to enter the respective value for Long Diagonal of Parallelogram, Short Diagonal of Parallelogram & Obtuse Angle between Diagonals of Parallelogram 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 Long Edge of Parallelogram?

In this formula, Long Edge of Parallelogram uses Long Diagonal of Parallelogram, Short Diagonal of Parallelogram & Obtuse Angle between Diagonals of Parallelogram. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)))
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))

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