Suppose you leave home and hike 10 miles due north, then 8 miles in the direction 40° east of north,

Question

and then 6 miles due east.

(a) How far are you from home?

(b) What direction should you hike in
order to return home?

Answer 1

same vector stuff like pulling the car

east = 0 + 8 sin 40 + 6
north = 10 +8 cos 40 + 0

dist = sqrt(east^2 + north^2)
tan angle east of N = east/north
(note this is true compass rose angle, not math angle from x axis)

add or subtract 180 depending on if angle was less or more than 180