document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=617271>Question 617271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cruise ship sailed north for 50 km. Then, the captain turned the ship eastward through an angle of pi/6 and sailed an additional 50 km. Without using a calculator, determine an exact expression for the direct distance from the start to the finish of the cruise. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #388242 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=388242\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A cruise ship sailed north for 50 km. Then, the captain turned the ship eastward through an angle of pi/6 and sailed an additional 50 km. Without using a calculator, determine an exact expression for the direct distance from the start to the finish of the cruise.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "&#960;/6 = 30 deg = turn from north towards the east.<BR>\n" );
document.write( "supplementary angle (inside triangle formed) = (180 - 30) = 150 deg<BR>\n" );
document.write( ".<BR>\n" );
document.write( "This forms a 50 Km, 50 Km, side_c triangle with the angle between the<BR>\n" );
document.write( "two 50 Km sides = 150 deg.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "use the law of cosines: where C = 150 deg<BR>\n" );
document.write( ".<BR>\n" );
document.write( "c² = a² + b² &#8722; 2abcos[C]<BR>\n" );
document.write( "c² = (50)² + (50)² &#8722; 2(50)(50)cos[150]&#8195;...&#8195;cos[150] = (-&#8730;3)/2<BR>\n" );
document.write( "c² = 5000 + 2500(&#8730;3)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2+%2B+b%5E2+-+2ab%2Acos%28C%29 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2+%2B+b%5E2+-+2ab%2Acos%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+50%5E2+%2B+50%5E2+-+2%2A50%2A50%2Acos%28pi%2F6%29 ALIGN=MIDDLE  ALT=\"c%5E2+=+50%5E2+%2B+50%5E2+-+2%2A50%2A50%2Acos%28pi%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+2500+%2B+2500+-+100%2A50%2A%28-sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"c%5E2+=+2500+%2B+2500+-+100%2A50%2A%28-sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+5000+-+5000%2A%28-sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"c%5E2+=+5000+-+5000%2A%28-sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+5000+%2B+5000%2A%28sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"c%5E2+=+5000+%2B+5000%2A%28sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+5000+%2B+2500%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"c%5E2+=+5000+%2B+2500%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%285000+%2B+2500%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"c+=+sqrt%285000+%2B+2500%2Asqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );