The formula to calculate the Inradius of a Rhombus given its area and acute angle is:
\[ \text{Inradius} = \frac{\sqrt{\text{Area} \times \sin(\text{Acute Angle})}}{2} \]
The Inradius of a Rhombus is defined as the radius of the circle which is inscribed inside the rhombus. The Area of a Rhombus is the amount of two-dimensional space occupied by the rhombus. The Acute Angle of a Rhombus is the angle inside the rhombus which is less than 90 degrees.
Let's assume the following values:
Using the formula:
\[ \text{Inradius} = \frac{\sqrt{70 \times \sin(0.785398163397301)}}{2} \approx 3.51772208549265 \, \text{meters} \]
The Inradius of the Rhombus is approximately 3.51772208549265 meters.
| Area (square meters) | Acute Angle (radians) | Inradius (meters) |
|---|---|---|
| 60 | 0.7853981633973 | 3.256777812162913 |
| 65 | 0.7853981633973 | 3.389761819697618 |
| 70 | 0.7853981633973 | 3.517722085492650 |
| 75 | 0.7853981633973 | 3.641188287804658 |
| 80 | 0.7853981633973 | 3.760603093086116 |