A ship sails from Port A, 60 nautical miles due west , to a port B . It then proceeds a distance of 50 nautical miles on a bearin of 210 derees to a Port C??

Find the distance and bearin of C from A...

Help would be appreciated

Drawing a sketch will be helpful. Then apply the law of cosines, followed by the law of sines.

I know I've got to use those rules but I'm strugling to draw the sketch... lke how do you draw the bearing of 210

If you make your sketch, you will see a triangle with angle 120 degrees (90+30 degrees).

Bearings, in this case, turn clockwise off the positive y-axis. 180 degrees is south, or down the negative y-axis. Then, 30 degrees more.

That is, if we were to stand and B and face A, then turn 120 degrees to the right we will be facing C.

One side is length 60 and the other length 50.

Find the distance from A to C by using the law of cosines.

AC=\sqrt{(AB)^{2}+(BC)^{2}-2(AB)(BC)cos(120)}

Plug in your given values and find AC.