The formula to calculate the circumradius of a rectangle given its length and the acute angle between the diagonals is:
\[ \text{Circumradius} = \frac{\text{Length}}{2 \cdot \cos\left(\frac{\text{Acute Angle}}{2}\right)} \]
The circumradius of a rectangle is the radius of the circle which contains the rectangle with all the vertices of the rectangle lying on the circle. The acute angle between the diagonals of the rectangle is the angle made by the diagonals which is less than 90 degrees.
Let's assume the following values:
Using the formula:
\[ \text{Circumradius} = \frac{8}{2 \cdot \cos\left(\frac{1.2217304763958}{2}\right)} \approx 4.8831 \, \text{meters} \]
The circumradius is approximately 4.8831 meters.
| Length (meters) | Acute Angle (radians) | Circumradius (meters) |
|---|---|---|
| 6 | 1 | 3.418481781973647 |
| 6 | 1.1 | 3.518960361108066 |
| 6 | 1.2 | 3.634884943536950 |
| 6 | 1.3 | 3.768447499456473 |
| 6 | 1.4 | 3.922377779200783 |
| 7 | 1 | 3.988228745635922 |
| 7 | 1.1 | 4.105453754626078 |
| 7 | 1.2 | 4.240699100793109 |
| 7 | 1.3 | 4.396522082699219 |
| 7 | 1.4 | 4.576107409067579 |
| 8 | 1 | 4.557975709298196 |
| 8 | 1.1 | 4.691947148144089 |
| 8 | 1.2 | 4.846513258049267 |
| 8 | 1.3 | 5.024596665941965 |
| 8 | 1.4 | 5.229837038934376 |
| 9 | 1 | 5.127722672960471 |
| 9 | 1.1 | 5.278440541662100 |
| 9 | 1.2 | 5.452327415305426 |
| 9 | 1.3 | 5.652671249184710 |
| 9 | 1.4 | 5.883566668801174 |
| 10 | 1 | 5.697469636622746 |
| 10 | 1.1 | 5.864933935180111 |
| 10 | 1.2 | 6.058141572561584 |
| 10 | 1.3 | 6.280745832427455 |
| 10 | 1.4 | 6.537296298667971 |