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

Formula

The formula to calculate the Long Edge of Parallelogram is:

$eLong = \frac{1}{2} \sqrt{dLong^2 + dShort^2 + (2 \cdot dLong \cdot dShort \cdot \cos(\angle d(Acute)))}$

Definition

Long Edge of Parallelogram is the length of the longest pair of parallel sides in a 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 degrees.

Example Calculation

Let's assume the following values:

Long Diagonal = 18 Meters
Short Diagonal = 9 Meters
Acute Angle = 0.872664625997001 Radians

Using the formula:

$eLong = \frac{1}{2} \sqrt{18^2 + 9^2 + (2 \cdot 18 \cdot 9 \cdot \cos(0.872664625997001))} = 12.3820756089042$

The Long Edge is 12.3820756089042 Meters.

Conversion Chart

Long Diagonal (Meters)	Short Diagonal (Meters)	Acute Angle (Radians)	Long Edge (Meters)
15	9	0.872664625997	10.949345352752825
16	9	0.872664625997	11.425003627896135
17	9	0.872664625997	11.902657356280985
18	9	0.872664625997	12.382075608904181
19	9	0.872664625997	12.863061090899391
20	9	0.872664625997	13.345444348982909