Adog searching for a bone walks 3.5 m south, then 8.2 m at an angle of 30.° north of east, and finally 15 m west. what was the dog's resultant displacement.

First, we resolve the diagonal movement in to components of north and east.
north = 8.2sin(30)
north = 4.1 m

east = 8.2cos(30)
east = 7.1

Vertical movement: 4.1 - 3.5 = 0.6 m north
Horizontal movement: 15 - 7.1 = 7.9 m west

Magnitude = √(0.6² + 7.9²)
Magnitude = 7.92 m

Direction:
tan∅ = y/x
tan∅ = 0.6 / 7.92
∅ = 4.33°

The dog walks 7.92 meters at an angle of 4.33° from south