POSSIBLE POINTS: 11.11
A hiker walks $5 \mathrm{~km}$ south and then $12 \mathrm{~km}$ east. Determine the angle and direction of the total displacement of the hiker from the starting point

Step 1 ：Calculate the magnitude of vector A: \( |A| = 5 \) km

Step 2 ：Calculate the magnitude of vector B: \( |B| = 12 \) km

Step 3 ：Calculate the magnitude of the total displacement: \( |C| = \sqrt{A^2 + B^2} = \sqrt{(5 \, \text{km})^2 + (12 \, \text{km})^2} \)

Step 4 ：Simplify the magnitude of the total displacement: \( |C| = \sqrt{169 \, \text{km}^2} \)

Step 5 ：Find the angle of the total displacement: \( \theta = \arctan\left(\frac{5 \, \text{km}}{12 \, \text{km}}\right) \)

Step 6 ：Simplify the angle of the total displacement: \( \theta \approx 22.62 \) degrees

Step 7 ：Determine the direction of the total displacement: southeast

Step 8 ：Final answer: The magnitude of the total displacement is \( \boxed{13} \) km and the angle is approximately \( \boxed{22.62} \) degrees southeast.