An airplane leaves an airport and flies due west 150 miles and then 220 miles in the direction s 69.83 degrees w. how far is the plane from the airport at this time?

1) Vector representation

a) 150 miles west = -150 i

b) 220 miles S68.93W

sin(68.93) = x/220 ==> x = 220[sin(68.93)] = 205.3
cos(68.93) = y/220 ==> y = 220[cos(68.93)] = 79.1

==> 220 miles S68.93 = -205.3 i - 79.1 j

c) Vectorial addition

r = -150i - 205.3 i - 79.1 j
r = -355i - 79.1 j

d) module

|r| = √[(350)^2 + (79.1)^2] = 370

370 miles