The formula to calculate Polar Distance is:
\[ D_{\text{polar}} = \sqrt{r_1^2 + r_2^2 - 2 \cdot r_1 \cdot r_2 \cdot \cos(\theta_2 - \theta_1)} \]
The Polar Distance between two points in a polar coordinate system can be calculated using the provided formula. This formula accounts for the radii \(r_1\) and \(r_2\) and the angles \(\theta_1\) and \(\theta_2\) (in degrees) of the two points.
Let's assume the following:
Step 1: Convert angles to radians:
\[ \theta_1 = 45^\circ \times \frac{\pi}{180} = 0.785 \, \text{radians} \]
\[ \theta_2 = 120^\circ \times \frac{\pi}{180} = 2.094 \, \text{radians} \]
Step 2: Calculate Polar Distance:
\[ D_{\text{polar}} = \sqrt{5^2 + 3^2 - 2 \cdot 5 \cdot 3 \cdot \cos(2.094 - 0.785)} \approx 5.17 \]
Therefore, the Polar Distance is approximately 5.17.
