posted by Dan .
An airplane flies 200 km due west from city A to city B and then 270 km in the direction of 31.0° north of west from city B to city C.
(a) In straight-line distance, how far is city C from city A?
(b) Relative to city A, in what direction is city C?
AC = 200 km @ 180o + 270 km @ 149o.
X=Hor.=200*cos180 + 270*cos149=-431.4 km
Y=Ver.=200*sin180 + 270*sin149=139.1 km.
a. (AC)^2 = X^2 + Y^2 = 205,454.77
AC = 453.3 km.
b. tanA = Y/X = 139.1/431.4 = 0.32244
A = 17.9o North of West.