SOLUTION: I have a trig problem on a ship's bearing and I really don't understand ship's bearings. I think they are measured in degrees from north clockwise on the circle of the compass and

Question 499190: I have a trig problem on a ship's bearing and I really don't understand ship's bearings. I think they are measured in degrees from north clockwise on the circle of the compass and expressed as W/N or S/N.
My proplem is: "A ship starts from a given point and sails 5km on a bearing of 45 degrees and then 6km on a bearing of 60 degrees. Find it's distance and bearing from its starting point."
I have drawn two circles of radii 5 and 6. I'm not sure I draew them in the right relation to each other. The center of the second circle is on the circumfrence of the first circle 45 degrees from north (360). I drew the radius of the second circle 60 degrees from the 360 degree mark of the second circle. I am unsure how to proceed from here. I am looking for a place to apply the law of cosines.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Most word problems have a lot of information in them that you do not need. The heart of this problem has nothing to do with ships or compass directions. Using graph paper, put a point a (0,0). That is where the ship is starting.
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45 degrees is where you expect it to be. It's midway between the y-axis and the x-axis. You could put a point at (10,10) and draw a straight line through the origin.
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The ship goes for a while along this 45 degree line. 5 km in fact. This 45-degree bearing is called northeast (NE). A bearing of 90 is called East; 135 is called SE; 180 is called S; etc. But that does not affect how you do the math.
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Then it turns to a bearing of 60 degrees. That means it turns 15 degrees toward the y-axis. If you were to put a protractor on the paper with the base parallel to the x-axis, you could draw the line at 60 degrees.
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It continues on this new line for 6 km. Measure that and plot the point.
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Now draw a line from that point back to the origin, (0,0).
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This results in a triangle. The longest side extends from the origin to the point on the 60-degree line. That is the furtherest point the ship has traveled.
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You can use your knowledge of complementary and supplementary angles to determine the angle between the two lines that the ship traveled. (My mental visualization is that this interior angle is about 75 degrees. But you should check it with your graph.)
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That gives you a side, an angle, and a side. Trig has the calculation rules for the third side of a triangle when you know SAS. (Hint: Study the Law of Cosines.)
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Use your graph to check your work.
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Done.
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