A hiker begins her trip away from her car by first walking $34\mathrm{.}0$ km south. She stops and sets up her tent for the night. On the second day, she walks $21\mathrm{.}0$ km in a direction that makes an angle of $28\mathrm{.}0$ degrees north of east, at which point she discovers a forest ranger's tower. Determine the magnitude of her total displacement.