an airplane flies 200 km due west from city A and then 350 km in the direction of 32.0 degrees north of west from city B to city C.

Question

a) in a straight-line distance, how far is city c from city a?
b) relative to city a, what direction is city c?

Answer 1

a. 32 deg North of West = 148 deg.,CCW.

X=hor. = -200 + 350cos148 = -496.82km.
Y = ver. = 350sin148 = 185.47km.

d = sqrt(X^2+Y^2),
d = sqrt((-496.82)^2 + (185.47)^2 =
530.3km.

b. tanA = Y / X = 185.47 / -496.82 = -0.37332.
A = -20.47 deg,CW. = 180 - 20.47 = 159.53 deg.,CCW. = 20.47 deg, North of West..