document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=826255>Question 826255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sir/Madam;<BR>\n" );
document.write( "    A pleasant day! Kindly help me with this word problem about Law of Cosines.  here it is:<BR>\n" );
document.write( "    Two ships leave harbor at 9:00 AM in the directions S 72°W and S 25°E at 27 kph and 35 kph respectively.  How far apart are they at 9:55 AM? <BR>\n" );
document.write( "    Thank you very much for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497974 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=497974\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note that both angles are measured from the y axis south of the x axis.  72 degrees south west is measured clockwise from the y axis and 25 degrees south east is measured from the y axis counter clockwise.<BR>\n" );
document.write( "We use rate * time = distance to calculate two sides of our triangle and note that the third side is the distance between our two ships.<BR>\n" );
document.write( "Note that both ships are sailing for 55 minutes and the rates are given in kilometers per hour.<BR>\n" );
document.write( "side 1 = 27 * 55/60 = 24.75<BR>\n" );
document.write( "side 2 = 35 * 55/60 = 32.08<BR>\n" );
document.write( "also add 72 and 25 to get the angle between side 1 and side 2 and <BR>\n" );
document.write( "we have side angle side (SAS) information about the triangle<BR>\n" );
document.write( "we can now use the law of cosines<BR>\n" );
document.write( "c^2 = a^2 +b^2 - 2ab * cosine(C) <BR>\n" );
document.write( "c^2 = (24.75)^2 +(32.08)^2 - 2*(24.75)*(32.08)*cosine(97)<BR>\n" );
document.write( "c^2 = 612.56 + 1029.13 -  1587.96*(-0.12)<BR>\n" );
document.write( "c^2 = 1832.25<BR>\n" );
document.write( "c = 42.80<BR>\n" );
document.write( "our two ships are 42.8 kilometers apart after sailing for 55 minutes<BR>\n" );
document.write( "  </SPAN>\n" );
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