Question

an aircraft flies 500 km on a bearing of 100 degrees and then 600 km on a bearing of 160 degrees. find the distance and bearing of the finishing point from the starting point. give a relative figure.

Answer 1

 Let the starting point be A and the air craft travels 500km to reachat B.given bearing is 100deg.since the bearing is always calculated with north,<made by northat A and ABis 100 deg 
Again aircraft travels 600km from B to reach C on a bearing of 160 deg 
ie,angle made by BC with North at B is 160.<DBC=160 deg where D is a point on North at B 
Now <DBA = 80 degree(co interior angles are supplementary for 2 parallel lines ie, 2 norths and the transversal AB)If you draw the figure you can understand easily 
Hence <ABC = 120 deg {angle at a point is 360 360-(160+80)=360-240=120} 
Now in triangle ABC,use cosine formula b^2= a^2 + c^2 -2bc CosB 
= 600^2 +500^2 -2*600*500*Cos120 
Simply,you'll get b^2.then take square root of it,which will give the distance BC ie, the distance b/n starting and finishing pt.