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Problem:

The velocity of an aircraft is 200 km/hr due west. A northwest wind of 50 km/hr is blowing.

a. What is the velocity of the aircraft relative to the ground?

b. If the pilot's destination is due west, at what angle should he point his plane to get there?

c. If his destination is 400 km due west, how long will it take him to get there?

My correct answer:

G = 200

G

_{x}= 200*cos(180°) = -200

G

_{y}= 200*sin(180°) = 0

G

_{θ}= 180°

---

W = 50

W

_{x}= 50*cos(315°) = 35.36

W

_{y}= 50*sin(315°) = -35.36

W

_{θ}= 315°

∴

R = √[(-35.46)

^{2}+(-164.64)

^{2}] = 168.4

R

_{x}= -164.64

R

_{y}= -35.36

R

_{θ}= arctan[(-35.36)/(-164.64)] = 12.12°

...And I also solved step C, but it's not relevant.

The book says the plane is moving 168.4 km/hr at 12.12° south of west...

I don't understand how they knew what the 12.12° meant...How did they know it was south of west, rather than north-east, which is the direction your average 12.12° on the unit circle would face?