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

✖Area of Parallelogram is the total quantity of plane enclosed by the boundary of the Parallelogram.ⓘ Area of Parallelogram [A]			+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%
✖Acute Angle between Diagonals of Parallelogram is the angle made by the diagonals of the Parallelogram which is less than 90 degree.ⓘ Acute Angle between Diagonals of Parallelogram [∠_d(Acute)]			+10% -10%

✖Long Diagonal of Parallelogram is the length of the line joining the pair of acute angle corners of a Parallelogram.ⓘ Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals [d_Long]

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

STEP 0: Pre-Calculation Summary

Formula Used

Long Diagonal of Parallelogram = (2*Area of Parallelogram)/(Short Diagonal of Parallelogram*sin(Acute Angle between Diagonals of Parallelogram))
d_Long = (2*A)/(d_Short*sin(∠_d(Acute)))
This formula uses 1 Functions, 4 Variables

Functions Used

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., sin(Angle)

Variables Used

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.
Area of Parallelogram - (Measured in Square Meter) - Area of Parallelogram is the total quantity of plane enclosed by the boundary of the 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.
Acute Angle between Diagonals of Parallelogram - (Measured in Radian) - Acute Angle between Diagonals of Parallelogram is the angle made by the diagonals of the Parallelogram which is less than 90 degree.

STEP 1: Convert Input(s) to Base Unit

Area of Parallelogram: 60 Square Meter --> 60 Square Meter No Conversion Required
Short Diagonal of Parallelogram: 9 Meter --> 9 Meter No Conversion Required
Acute Angle between Diagonals of Parallelogram: 50 Degree --> 0.872664625997001 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_Long = (2*A)/(d_Short*sin(∠_d(Acute))) --> (2*60)/(9*sin(0.872664625997001))

Evaluating ... ...

d_Long = 17.4054305244328

STEP 3: Convert Result to Output's Unit

17.4054305244328 Meter --> No Conversion Required

FINAL ANSWER

17.4054305244328 ≈ 17.40543 Meter <-- Long Diagonal of Parallelogram

(Calculation completed in 00.020 seconds)

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Birsa Institute of Technology (BIT), Sindri

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< Long Diagonal of Parallelogram Calculators

Long Diagonal of Parallelogram given Sides and Obtuse Angle between sides

LaTeX Go 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 given Sides and Acute Angle between Sides

LaTeX Go 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 given Area, Short Diagonal and Acute Angle between Diagonals

LaTeX Go Long Diagonal of Parallelogram = (2*Area of Parallelogram)/(Short Diagonal of Parallelogram*sin(Acute Angle between Diagonals of Parallelogram))

Long Diagonal of Parallelogram

LaTeX Go Long Diagonal of Parallelogram = sqrt((2*Long Edge of Parallelogram^2)+(2*Short Edge of Parallelogram^2)-Short Diagonal of Parallelogram^2)

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

LaTeX Go

Long Diagonal of Parallelogram = (2*Area of Parallelogram)/(Short Diagonal of Parallelogram*sin(Acute Angle between Diagonals of Parallelogram))
d_Long = (2*A)/(d_Short*sin(∠_d(Acute)))

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 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 calculator uses Long Diagonal of Parallelogram = (2*Area of Parallelogram)/(Short Diagonal of Parallelogram*sin(Acute Angle between Diagonals of Parallelogram)) to calculate 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 calculate Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals using this online calculator? To use this online calculator 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. Here is how the Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals calculation can be explained with given input values -> 17.40543 = (2*60)/(9*sin(0.872664625997001)).

FAQ

What is 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 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 and is represented as d_Long = (2*A)/(d_Short*sin(∠_d(Acute))) or Long Diagonal of Parallelogram = (2*Area of Parallelogram)/(Short Diagonal of Parallelogram*sin(Acute Angle between Diagonals of Parallelogram)). Area of Parallelogram is the total quantity of plane enclosed by the boundary of the Parallelogram, Short Diagonal of Parallelogram is the length of the line joining the pair of obtuse angle corners of a Parallelogram & Acute Angle between Diagonals of Parallelogram is the angle made by the diagonals of the Parallelogram which is less than 90 degree.

How to calculate 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 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 is calculated using Long Diagonal of Parallelogram = (2*Area of Parallelogram)/(Short Diagonal of Parallelogram*sin(Acute Angle between Diagonals of Parallelogram)). To calculate Long Diagonal of Parallelogram given Area, Short Diagonal and Acute Angle between Diagonals, you need Area of Parallelogram (A), Short Diagonal of Parallelogram (d_Short) & Acute Angle between Diagonals of Parallelogram (∠_d(Acute)). With our tool, you need to enter the respective value for Area of Parallelogram, Short Diagonal of Parallelogram & Acute 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 Diagonal of Parallelogram?

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

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)

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