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

Answer: 370 miles