Short Edge of Parallelogram given Diagonals and Acute 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%
✖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%

✖Short Edge of Parallelogram is the length of the shortest pair of parallel edges in a Parallelogram.ⓘ Short Edge of Parallelogram given Diagonals and Acute Angle between Diagonals [e_Short]

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

STEP 0: Pre-Calculation Summary

Formula Used

Short 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)))
e_Short = 1/2*sqrt(d_Long^2+d_Short^2-(2*d_Long*d_Short*cos(∠_d(Acute))))
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

Short Edge of Parallelogram - (Measured in Meter) - Short Edge of Parallelogram is the length of the shortest pair of parallel edges 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.
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

Long Diagonal of Parallelogram: 18 Meter --> 18 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

e_Short = 1/2*sqrt(d_Long^2+d_Short^2-(2*d_Long*d_Short*cos(∠_d(Acute)))) --> 1/2*sqrt(18^2+9^2-(2*18*9*cos(0.872664625997001)))

Evaluating ... ...

e_Short = 7.01314505877215

STEP 3: Convert Result to Output's Unit

7.01314505877215 Meter --> No Conversion Required

FINAL ANSWER

7.01314505877215 ≈ 7.013145 Meter <-- Short Edge of Parallelogram

(Calculation completed in 00.015 seconds)

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Created by Anamika Mittal

Vellore Institute of Technology (VIT), Bhopal

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< Short Edge of Parallelogram Calculators

Short Edge of Parallelogram given Diagonals and Obtuse Angle between Diagonals

LaTeX Go Short 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)))

Short Edge of Parallelogram given Diagonals and Long Edge

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

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

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

Short Edge of Parallelogram

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

Short Edge of Parallelogram given Diagonals and Acute 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 Short Edge of Parallelogram given Diagonals and Acute Angle between Diagonals?

Short Edge of Parallelogram given Diagonals and Acute Angle between Diagonals calculator uses Short 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 calculate the Short Edge of Parallelogram, Short Edge of Parallelogram given Diagonals and Acute Angle between Diagonals formula is defined as the length of the shortest pair of parallel edges in a Parallelogram, and calculated using diagonals and acute angle between diagonals of the Parallelogram. Short Edge of Parallelogram is denoted by e_Short symbol.

How to calculate Short Edge of Parallelogram given Diagonals and Acute Angle between Diagonals using this online calculator? To use this online calculator for Short 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. Here is how the Short Edge of Parallelogram given Diagonals and Acute Angle between Diagonals calculation can be explained with given input values -> 7.013145 = 1/2*sqrt(18^2+9^2-(2*18*9*cos(0.872664625997001))).

FAQ

What is Short Edge of Parallelogram given Diagonals and Acute Angle between Diagonals?

Short Edge of Parallelogram given Diagonals and Acute Angle between Diagonals formula is defined as the length of the shortest pair of parallel edges in a Parallelogram, and calculated using diagonals and acute angle between diagonals of the Parallelogram and is represented as e_Short = 1/2*sqrt(d_Long^2+d_Short^2-(2*d_Long*d_Short*cos(∠_d(Acute)))) or Short 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 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 & 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 Short Edge of Parallelogram given Diagonals and Acute Angle between Diagonals?

Short Edge of Parallelogram given Diagonals and Acute Angle between Diagonals formula is defined as the length of the shortest pair of parallel edges in a Parallelogram, and calculated using diagonals and acute angle between diagonals of the Parallelogram is calculated using Short 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 calculate Short Edge of Parallelogram given Diagonals and Acute Angle between Diagonals, you need Long Diagonal of Parallelogram (d_Long), 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 Long Diagonal 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 Short Edge of Parallelogram?

In this formula, Short Edge of Parallelogram uses Long Diagonal 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 -

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

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