document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125459>Question 1125459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cargo boats leave the same port at the same time. The direction of one boat is at an angle of 30 degrees to the other. If the ratio of the speed of the first boat to the second is sqrt 3 over 2, and if the second boat travels at 18km/h, how far apart, in km, are they at the end of 5 hours? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741812 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=741812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two cargo boats leave the same port at the same time.<BR>\n" );
document.write( " The direction of one boat is at an angle of 30 degrees to the other.<BR>\n" );
document.write( " If the ratio of the speed of the first boat to the second is sqrt 3 over 2, and if the second boat travels at 18km/h, how far apart, in km, are they at the end of 5 hours?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the speed of the 1st boat (s)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%2F18 ALIGN=MIDDLE  ALT=\"s%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiply <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2s+=+18%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"2s+=+18%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31.177%2F2 ALIGN=MIDDLE  ALT=\"31.177%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 15.6 km/h is the speed of the 2nd boat<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the distance each has traveled in 5 hrs<BR>\n" );
document.write( "5*15.6 = 78 km traveled by the 1st boat<BR>\n" );
document.write( "5*18 = 90 km by the 2nd boat<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The distance between the boat is the side (a) opposite the 30 degree angle (A)<BR>\n" );
document.write( "Use the law of cosines: a^2 = b^2 + c2 - 2bc*Cos(a),where<BR>\n" );
document.write( "b = 78<BR>\n" );
document.write( "c = 90<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+78%5E2+%2B+90%5E2+-+2%2878%2A90%29%2ACos%2830%29 ALIGN=MIDDLE  ALT=\"a%5E2+=+78%5E2+%2B+90%5E2+-+2%2878%2A90%29%2ACos%2830%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a^2 = 6084 + 8100 - 2(7020)*.866<BR>\n" );
document.write( "Do the math<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282025%29 ALIGN=MIDDLE  ALT=\"sqrt%282025%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 45 km apart in 5 hrs<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );