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

✖Long Edge of Parallelogram is the length of the longest pair of parallel sides in a Parallelogram.ⓘ Long Edge of Parallelogram [e_Long]			+10% -10%
✖Short Edge of Parallelogram is the length of the shortest pair of parallel edges in a Parallelogram.ⓘ Short Edge of Parallelogram [e_Short]			+10% -10%
✖Acute Angle of Parallelogram is the measure of pair of opposite angles which are less than 90 degree in a Parallelogram.ⓘ Acute Angle of Parallelogram [∠_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 Sides and Acute Angle between Sides [d_Long]

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
d_Long = sqrt(e_Long^2+e_Short^2+(2*e_Long*e_Short*cos(∠_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

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.
Long Edge of Parallelogram - (Measured in Meter) - Long Edge of Parallelogram is the length of the longest pair of parallel sides in a Parallelogram.
Short Edge of Parallelogram - (Measured in Meter) - Short Edge of Parallelogram is the length of the shortest pair of parallel edges in a Parallelogram.
Acute Angle of Parallelogram - (Measured in Radian) - Acute Angle of Parallelogram is the measure of pair of opposite angles which are less than 90 degree in a Parallelogram.

STEP 1: Convert Input(s) to Base Unit

Long Edge of Parallelogram: 12 Meter --> 12 Meter No Conversion Required
Short Edge of Parallelogram: 7 Meter --> 7 Meter No Conversion Required
Acute Angle of Parallelogram: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_Long = sqrt(e_Long^2+e_Short^2+(2*e_Long*e_Short*cos(∠_Acute))) --> sqrt(12^2+7^2+(2*12*7*cos(0.785398163397301)))

Evaluating ... ...

d_Long = 17.6576878225706

STEP 3: Convert Result to Output's Unit

17.6576878225706 Meter --> No Conversion Required

FINAL ANSWER

17.6576878225706 ≈ 17.65769 Meter <-- Long Diagonal of Parallelogram

(Calculation completed in 00.004 seconds)

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Created by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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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 Sides and Acute Angle between Sides 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 Diagonal of Parallelogram given Sides and Acute Angle between Sides?

Long Diagonal of Parallelogram given Sides and Acute Angle between Sides calculator 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(Acute Angle of Parallelogram))) to calculate the Long Diagonal of Parallelogram, Long Diagonal of Parallelogram given Sides and Acute Angle between Sides formula is defined as the length of the line joining the pair of acute angle corners of a Parallelogram, and calculated using sides and acute angle between sides of the Parallelogram. Long Diagonal of Parallelogram is denoted by d_Long symbol.

How to calculate Long Diagonal of Parallelogram given Sides and Acute Angle between Sides using this online calculator? To use this online calculator for Long Diagonal of Parallelogram given Sides and Acute Angle between Sides, enter Long Edge of Parallelogram (e_Long), Short Edge of Parallelogram (e_Short) & Acute Angle of Parallelogram (∠_Acute) and hit the calculate button. Here is how the Long Diagonal of Parallelogram given Sides and Acute Angle between Sides calculation can be explained with given input values -> 17.65769 = sqrt(12^2+7^2+(2*12*7*cos(0.785398163397301))).

FAQ

What is Long Diagonal of Parallelogram given Sides and Acute Angle between Sides?

Long Diagonal of Parallelogram given Sides and Acute Angle between Sides formula is defined as the length of the line joining the pair of acute angle corners of a Parallelogram, and calculated using sides and acute angle between sides of the Parallelogram and is represented as d_Long = sqrt(e_Long^2+e_Short^2+(2*e_Long*e_Short*cos(∠_Acute))) or 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 Edge of Parallelogram is the length of the longest pair of parallel sides in a Parallelogram, Short Edge of Parallelogram is the length of the shortest pair of parallel edges in a Parallelogram & Acute Angle of Parallelogram is the measure of pair of opposite angles which are less than 90 degree in a Parallelogram.

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

Long Diagonal of Parallelogram given Sides and Acute Angle between Sides formula is defined as the length of the line joining the pair of acute angle corners of a Parallelogram, and calculated using sides and acute angle between sides of the Parallelogram is calculated using 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))). To calculate Long Diagonal of Parallelogram given Sides and Acute Angle between Sides, you need Long Edge of Parallelogram (e_Long), Short Edge of Parallelogram (e_Short) & Acute Angle of Parallelogram (∠_Acute). With our tool, you need to enter the respective value for Long Edge of Parallelogram, Short Edge of Parallelogram & Acute Angle 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 Long Edge of Parallelogram, Short Edge of Parallelogram & Acute Angle of Parallelogram. We can use 3 other way(s) to calculate the same, which is/are as follows -

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(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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