Question 499190
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.