document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40736>Question 40736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Latitude presents special mathematical considerations for cartographers. Latitude is the north-south location on the earth between the equator and the poles. Since the earth flattens slightly at the poles, a nautical mile varies with latitude. A nautical mile is given by N(e) = 6066 - 31 * cosine 2e. e represents the latitude in degrees. \r<BR>\n" );
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document.write( "•What is the length of a British nautical mile at Chicago (latitude of 42 degrees)? \r<BR>\n" );
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document.write( "•What is the length of a British nautical mile at the North Pole (latitude of 90 degrees)? \r<BR>\n" );
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document.write( "•Express N(e) in terms of cosine e only, do not use the double angle. \r<BR>\n" );
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document.write( "•At what latitude north is the length of a British nautical mile found to be 6040 feet? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26171 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=26171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%28e%29+=+6066+-+31%2Acos%282e%29+ ALIGN=MIDDLE  ALT=\"+N%28e%29+=+6066+-+31%2Acos%282e%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Chicago (42degrees):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%28e%29+=+6066+-+31cos%282e%29+ ALIGN=MIDDLE  ALT=\"+N%28e%29+=+6066+-+31cos%282e%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%28e%29+=+6066+-+31cos%282%2A42%29+ ALIGN=MIDDLE  ALT=\"+N%28e%29+=+6066+-+31cos%282%2A42%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%28e%29+=+6066+-+31cos%2884%29+ ALIGN=MIDDLE  ALT=\"+N%28e%29+=+6066+-+31cos%2884%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "N(e) = 6062.76 feet\r<BR>\n" );
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document.write( "North Pole (90 degrees):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%28e%29+=+6066+-+31cos%282e%29+ ALIGN=MIDDLE  ALT=\"+N%28e%29+=+6066+-+31cos%282e%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%28e%29+=+6066+-+31cos%282%2A90%29+ ALIGN=MIDDLE  ALT=\"+N%28e%29+=+6066+-+31cos%282%2A90%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%28e%29+=+6066+-+31cos%28180%29+ ALIGN=MIDDLE  ALT=\"+N%28e%29+=+6066+-+31cos%28180%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%28e%29+=+6066+%2B+31+ ALIGN=MIDDLE  ALT=\"+N%28e%29+=+6066+%2B+31+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "N(e) = 6097 feet\r<BR>\n" );
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document.write( "TRIG IDENTITY: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%282e%29+=+2cos%5E2%28e%29+-+1+ ALIGN=MIDDLE  ALT=\"+cos%282e%29+=+2cos%5E2%28e%29+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > so we then get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%28e%29+=+6066+-+31%282cos%5E2%28e%29+-+1%29+ ALIGN=MIDDLE  ALT=\"+N%28e%29+=+6066+-+31%282cos%5E2%28e%29+-+1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%28e%29+=+6066+-+62cos%5E2%28e%29+%2B+31+ ALIGN=MIDDLE  ALT=\"+N%28e%29+=+6066+-+62cos%5E2%28e%29+%2B+31+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%28e%29+=+6097+-+62cos%5E2%28e%29+ ALIGN=MIDDLE  ALT=\"+N%28e%29+=+6097+-+62cos%5E2%28e%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When nautical mile = 6040feet:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%28e%29+=+6066+-+31cos%282e%29+ ALIGN=MIDDLE  ALT=\"+N%28e%29+=+6066+-+31cos%282e%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6040+=+6066+-+31cos%282e%29+ ALIGN=MIDDLE  ALT=\"+6040+=+6066+-+31cos%282e%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-26+=+-+31cos%282e%29+ ALIGN=MIDDLE  ALT=\"+-26+=+-+31cos%282e%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-26%29%2F%28-31%29+=+cos%282e%29+ ALIGN=MIDDLE  ALT=\"+%28-26%29%2F%28-31%29+=+cos%282e%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2826%29%2F%2831%29+=+cos%282e%29+ ALIGN=MIDDLE  ALT=\"+%2826%29%2F%2831%29+=+cos%282e%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2e+=+cos%5E%28-1%29%28%2826%29%2F%2831%29%29+ ALIGN=MIDDLE  ALT=\"+2e+=+cos%5E%28-1%29%28%2826%29%2F%2831%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2e = 33 degrees to 2significant places<BR>\n" );
document.write( "--> e = 33/2<BR>\n" );
document.write( "--> e = 16.5 degrees latitide\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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