



 
Hi Sugar, Her is my diagram (not to scale). The sails from O to A then from A to B and finally from B to C. I am going to use vectors to show you one way to approach this problem. On the first leg of the trip the ship travels at i mi/hr for 6 hours and hence it goes 6i miles. Thus the vector v_{1} is given by
On the second leg of the trip the ship travels for 8 hours and hence it goes 8i miles. Thus the length of the line segment AB is 8i miles. The angle BAS has measure 90  50 = 40 degrees and hence the vector v_{2} is given by
Thus the vector from O to B is given by
On the last leg of the trip the ship travels for 10 hours and hence the distance from B to C is 10i miles. The angle RBC has measure 90 + 62 = 152 degrees and thus you can use the sine and cosine function again to find the vector v_{3}. The vector from O to C is then v_{1} + v_{2} + v_{3}. This gives the coordinates of C from which you can calculate the bearing of OC. Harley  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 