physics
posted by Carol .
A car is driven 165 km west and then 25 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?

Since no starting point was given, I assumed the trip started at the Origin.
Therefore, we'll subtract 0 from the vector sum to get the displacement.
Southwest = 45 deg. west of South = 225 deg CCW from 0 deg.
X = Hor. = 165 + 165*cos225,
X = 165 + 17.7 = 182.7 km,
Y = Ver. = 25*sin225 = 17.7 km.
tanA = 17.7 / 182.7 = 0.0969,
A = 5.53 deg,
D = 182.7 + i17.7,
D = 182.7 / cos5.53 = 183.6 km @
5.53 deg South of West.
D = 182.7 +i17.7, 
CORRECTION!
X = Hor. = 165 + 25*cos225.
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