Your dog is running around the grass in your backyard. he undergoes successive displacements, 3.60 m south, 8.46 m northeast, and 15.6 m west. what is the resultant displacement? (take + x direction to be east). find magnitud? find direction?

First, we resolve the northeast displacement into its north and east components. The angle from the positive x-axis of a northeast displacement is 45 degrees. Thus:
North = 8.46sin(45) = 5.98 m
East = 8.46cos(45) = 5.98 m

North displacement = 5.98 - 3.6 = 2.38 m
West displacement = 15.6 - 5.98 = 9.62

Magnitude = √(2.38² + 9.62²)
Magnitude = 9.91 m

Direction:
tan∅ = 2.38 / 9.62
∅ = 13.9° north from east