document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=329518>Question 329518</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following problem. Draw a diagram and show your work.\r<BR>\n" );
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document.write( "A ship travels a distance of 82 miles in the direction N 18degrees E and then travels 46 miles in the direction S 72degrees E. Find the distance and bearing of the ship's final position from its 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 #236277 by </B><A HREF=/tutors/aboutme.mpl?userid=galactus><B>galactus(183)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=galactus><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/cgi-bin/show-face.mpl?user=galactus><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=236277\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When the ship goes 18 degrees and then turns to a bearing of S72E, it turns 90 degrees. 72+18=90.\r<BR>\n" );
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document.write( "Another way to look at it, S72E is equal to an azimuth of 108 degrees and a bearing of N18E is equal to an azimuth of 18 degrees. 108-18=90. \r<BR>\n" );
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document.write( "So, we have a right triangle to deal with.\r<BR>\n" );
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document.write( "By Pythagoras, the distance back to the origin is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2882%5E2%2B46%5E2%29=2%2Asqrt%282210%29=94.02 ALIGN=MIDDLE  ALT=\"sqrt%2882%5E2%2B46%5E2%29=2%2Asqrt%282210%29=94.02\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles.\r<BR>\n" );
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document.write( "We can find the bearing from the origin to the ship by \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Barctan%2846%2F82%29=47.29 ALIGN=MIDDLE  ALT=\"18%2Barctan%2846%2F82%29=47.29\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees.\r<BR>\n" );
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document.write( "A bearing of N47.3E\r<BR>\n" );
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