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kookai18 · Aug 27, 2009, 05:42 PM

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

s_cianci · Aug 27, 2009, 05:45 PM

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

kookai18 · Aug 27, 2009, 08:24 PM

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

galactus · Aug 28, 2009, 09:36 AM

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.