An Aircraft departs from point A and flies 234 km on bearing

An Aircraft departs from point A and flies 234 km on bearing 73°, then 317 km on bearing 146 °, then 521 km on bearing 248 °, then 133 km on bearing 305 °. Find the final position of the aircraft.

Solution

First let us assume that it starts from origin.

Then it flies 234 km bearing 73 Degrees.

Hence position A = (234 cos 73, 234 sin 73) = (79.817, 223.775)

Next from that position it flies 317 bearing 146

i.e. position wrt A = (317 cos 146, 317 sin 146) = (-262.80, 177.264)

Hence from origin position of B is (-182.983,46.51)

From B it flies 521 km bearing 248

So C wrt B as origin would be (521 cos 248, 521 sin 248) = (-203.571, -483.062)

C position wrt origin = (-386.554, -436.512)

Next is from C to 133 km bearing 305

D position wrt C as origin = (133 cos 305, 133 sin 305)

= (76.286, -108.947)

D position wrt origin (starting point) = (-300.268, -545.459)