document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=460692>Question 460692</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane travels 160 miles at a heading of N 33 degrees W. It then changes direction and travels 205 miles at a heading of N 49 degrees W. How far is the plane from it's original position?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316032 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=316032\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A plane travels 160 miles at a heading of N 33 degrees W. It then changes direction and travels 205 miles at a heading of N 49 degrees W. How far is the plane from it's original position?<BR>\n" );
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document.write( "I don't have the means to draw a diagram which would be the best way to show you how to solve given problem so I will give it a try with words.<BR>\n" );
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document.write( "If you draw the given headings correctly you should get a triangle with sides of 205 and 160 and their included angle of 164º. The problem can then be solved with the Law of Cosines.<BR>\n" );
document.write( "let me describe what the diagram should look like:<BR>\n" );
document.write( "Starting from a point labeled A, travel a distance of 160 miles rotated 33º west of North. At the end of the 160 miles, labeled point B, travel a distance of 205 miles rotated 49º west of North at point B. Mark the end of 205 miles as point C. Connect point C to beginning point A to complete the  triangle. You now have a triangle with sides 160 & 205 with their included angle CBA. You can notice that this obtuse angle is made up of the complement of 49º=41º, the parallel angle of 33º plus 90º for a total of 41+33+90=164º<BR>\n" );
document.write( "solution: Using Law of Cosines: c^2=a^2+b^2-2abCosC<BR>\n" );
document.write( "let x= side CA<BR>\n" );
document.write( "x^2=120^2+205^2-2*160*205*cos164º<BR>\n" );
document.write( "x^2=14400+42025+63059=119484<BR>\n" );
document.write( "x=346 miles<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "The plane is 346 miles from its original position </SPAN>\n" );
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