Can someone explain how to work out bearings with distances?

Question

e.g. a plane flies 100km from point A on a bearing of 060 degrees to point B then it changes it's direction on a bearing of 195 degrees and flies fro 120km to point C what is the distance and bearing between points A and C

Answer 1

The problem is solved using Trigonometry and Pythagoras. First draw a rough triangle and drop a perpendicular from the position A which should be at the top. work out the distance from the position B to the position where the perpendicular cuts the base (B-C) and the height from base to position A. The distance from A to C is then worked out by applying Pythagoras to the distance the position where the vertical cuts the base to the height and you have the distance from A to C.

Answer 2

You can use Law of Cosines and Law of Sines for this solution, but breaking the vectors into components may be more comfortable:
100 @ 60° = 50√3 @ 0° + 50 @ 90°
120 @ 195° ≈ - 115.91 @ 0° -31.058 @ 90°
AC = 29.307 @ 180° + 18.942 @ 90°
AC = 34.896 km @ 122.88°

Answer 3

http://www.theingots.org/community/node/36