Find the resultant displacement vector as a distance and the bearing of this vector?

A ship sails 50 miles on a bearing of 20 degrees. It then goes 30 miles further on a bearing of 80 degrees. Find the resultant displacement vector as a distance and the bearing of this vector.





If you could show steps I would really appreciate it!|||Alright, what you do is figure out the y and x of each of the vectors first.





First vector:





y=sin(20)50


x=cos(20)50





Second vector





y=sin(80)30


x=cos(80)30





now you need the resultant. Add up the y's and x's





y (of resultant)= sin(80)30+sin(20)50





x(resultant) = cos(80)30+cos(20)50





then use pathagorean theorem.





sqrt( y(of resultant)^2 + x(resulant)^2)= final vector.





To find it's angle:





tan^-1(y/x)





and there you go!