The formula to calculate the obtuse angle between the diagonals of a rectangle is:
\[ \angle_d(\text{Obtuse}) = 2 \arctan\left(\frac{l}{b}\right) \]
Where:
The obtuse angle between the diagonals of a rectangle is the angle made by the diagonals which is greater than 90 degrees.
The length of the rectangle is any one of the pair of parallel sides which are longer than the remaining pair of parallel sides.
The breadth of the rectangle is any one of the pair of parallel sides which are shorter than the remaining pair of parallel sides.
Let's assume the following values:
Using the formula:
\[ \angle_d(\text{Obtuse}) = 2 \arctan\left(\frac{8}{6}\right) \approx 1.8546 \, \text{radians} \]
The obtuse angle is approximately 1.8546 radians.
| Length (meters) | Breadth (meters) | Obtuse Angle (radians) |
|---|---|---|
| 7 | 5 | 1.9011 |
| 7 | 6 | 1.7243 |
| 7 | 7 | 1.5708 |
| 8 | 5 | 2.0244 |
| 8 | 6 | 1.8546 |
| 8 | 7 | 1.7039 |
| 9 | 5 | 2.1274 |
| 9 | 6 | 1.9656 |
| 9 | 7 | 1.8195 |