Tammy leaves the office, drives 36 km due north.Then she turns onto a second highway and continues in direction 45 degree north of east for 50 km. What is her total displacement from the office? (give magnitude and direction)

Answer 1

Sketching the displacement vectors roughly to scale is a big help in seeing what needs to be done.
Draw the first arrow vertically on your page, with the arrow pointing up, and label it 35 km.
Start the next vector from the tip of that arrow, heading 45 ° clockwise from North; make it longer than the first vector; label it 50 km.
Join the tail of the first vector to the tip of the second vector, and that represents your resultant displacement (it points upward/rightward).

You should now see that the angle between the 35 km N and 50 km NE vectors is 45 ° + 90 ° = 135 °
Thus, you can use the cos law to find the magnitude of the resultant displacement.
Once you have this number, label it on your diagram.
You now need the direction of this vector, which will be the angle between it and the 35 km N vector. The sin law will help you here. The angle you find can be reported as N ___ ° E.

Answer 2

I agree, law of cosines is the way to go.