A hiker begins a trip by first walking 25.0 km 45.0° south of east from her base camp.On the second day she walks 40.0 km in a direction 60.0° north of east, at which point she discovers a forest ranger’s tower.Find the magnitude of the displacement from base camp.

Answer 1

You can draw a figure, and use the law of cosine/sines or..
figure components then add.
first day:
N: 25cos135 N (angles from 000 clockwise)
E: 2sin135 E

second day
N: 40cos30 N
E: 40sin30 E

Now add components:
N: 40cos30 + 25cos135
E: 40sin30 + 25sin135

Now, displacement..
d=sqrt(N^2 + E^2)

Answer 2

41.32