The formula to calculate the Long Diagonal of a Trapezoid is:
\[ d_{\text{Long}} = \sqrt{\text{Long Base}^2 + \text{Short Leg}^2 - 2 \cdot \text{Long Base} \cdot \text{Short Leg} \cdot \cos(\text{Larger Acute Angle})} \]
The Long Diagonal of a Trapezoid is the length of the line joining the corners of the smaller acute angle and the smaller obtuse angle of the trapezoid. The Long Base is the longer side among the pair of parallel sides, the Short Leg is the shorter side among the pair of non-parallel sides, and the Larger Acute Angle is the larger angle on the long base or the angle made by the long base and short leg.
Let's assume the following values:
Using the formula:
\[ d_{\text{Long}} = \sqrt{15^2 + 9^2 - 2 \cdot 15 \cdot 9 \cdot \cos(1.2217304763958)} \approx 14.6169 \]
The Long Diagonal is approximately 14.6169 Meters.
| Long Base (Meters) | Short Leg (Meters) | Larger Acute Angle (Radians) | Long Diagonal (Meters) |
|---|---|---|---|
| 14 | 9 | 1.2217304763958 | 13.813432733461905 |
| 14.5 | 9 | 1.2217304763958 | 14.212063277087667 |
| 15 | 9 | 1.2217304763958 | 14.616927218195038 |
| 15.5 | 9 | 1.2217304763958 | 15.027520754005895 |
| 16 | 9 | 1.2217304763958 | 15.443386892846560 |