The formula to calculate the acute angle between the diagonals of a rectangle is:
\[ \angle_d(\text{Acute}) = 2 \arctan\left(\frac{b}{l}\right) \]
Where:
The acute angle between the diagonals of a rectangle is the angle made by the diagonals which is less than 90 degrees.
The breadth of the rectangle is any one of the pair of parallel sides which are shorter than the remaining pair of parallel sides.
The length of the rectangle is any one of the pair of parallel sides which are longer than the remaining pair of parallel sides.
Let's assume the following values:
Using the formula:
\[ \angle_d(\text{Acute}) = 2 \arctan\left(\frac{6}{8}\right) \approx 1.2870 \, \text{radians} \]
The acute angle is approximately 1.2870 radians.
| Breadth (meters) | Length (meters) | Acute Angle (radians) |
|---|---|---|
| 5 | 7 | 1.2405 |
| 5 | 8 | 1.1172 |
| 5 | 9 | 1.0142 |
| 6 | 7 | 1.4173 |
| 6 | 8 | 1.2870 |
| 6 | 9 | 1.1760 |
| 7 | 7 | 1.5708 |
| 7 | 8 | 1.4377 |
| 7 | 9 | 1.3221 |