Question

An airplane starting from airport a flies 399 km east, then 552 km at 58.5 ◦ west 3 of north, and then 890 km north to arrive finally at airport
b. the next day, another plane flies directly from a to b in a straight line. in what direction should the pilot travel in this direct flight? use counterclockwise as the positive angular direction from due east, between the limits of −180◦ and 180◦ . assume there is no wind during these flights. answer in units of ◦ .

Answer 1

The approach here is to decompose all directions into North and East and then do simple Cartesian addition of the obtained coordinates.

S1 = 399 E

S2 = 552 Km 58.5 deg west of north ;

= 552 cos (58.5) N - 552 sin (58.5) E

= 288.41 N - 470.65 E

S3 = 890 N

total S = (890 + 288.41) N + (399 - 470.65) E

S = 1178.41 N - 71.65 E

D = $\sqrt{N^2 + E^2}$

D = 1180.58 Km

direction = atan(N/E) = -86.52 deg

means : 3.48 deg west of north