The formula to calculate the Short Diagonal of Parallelogram given Sides and Obtuse Angle between Sides is:
\[ d_{\text{Short}} = \sqrt{e_{\text{Long}}^2 + e_{\text{Short}}^2 + (2 \cdot e_{\text{Long}} \cdot e_{\text{Short}} \cdot \cos(\angle_{\text{Obtuse}}))} \]
The Short Diagonal of a Parallelogram is the length of the line joining the pair of obtuse angle corners of a Parallelogram. The Long Edge of a Parallelogram is the length of the longest pair of parallel sides in a Parallelogram. The Short Edge of a Parallelogram is the length of the shortest pair of parallel edges in a Parallelogram. The Obtuse Angle of a Parallelogram is the measure of the pair of opposite angles which are greater than 90 degrees in a Parallelogram.
Let's assume the following values:
Using the formula:
\[ d_{\text{Short}} = \sqrt{12^2 + 7^2 + (2 \cdot 12 \cdot 7 \cdot \cos(2.3561944901919))} = 8.61429397923665 \]
The Short Diagonal of the Parallelogram is 8.61429397923665 meters.
| Long Edge (meters) | Short Edge (meters) | Obtuse Angle (radians) | Short Diagonal (meters) |
|---|---|---|---|
| 10 | 7 | 2.3561944901919 | 7.071424936597108 |
| 10.5 | 7 | 2.3561944901919 | 7.436753536700256 |
| 11 | 7 | 2.3561944901919 | 7.817004266170010 |
| 11.5 | 7 | 2.3561944901919 | 8.210104032776718 |
| 12 | 7 | 2.3561944901919 | 8.614293979236654 |
| 12.5 | 7 | 2.3561944901919 | 9.028084696789749 |
| 13 | 7 | 2.3561944901919 | 9.450215120520042 |
| 13.5 | 7 | 2.3561944901919 | 9.879616306102276 |
| 14 | 7 | 2.3561944901919 | 10.315380307458295 |