document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110434>Question 1110434</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two ships leave Liverpool at the same time.  One of them travels north-west at an average speed of 10.5 km/h while the other travels at an average speed of 14 km/h on a bearing of 280&#5156;.  How far apart are these ships after 2 hours?\r<BR>\n" );
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document.write( "I do not understand this because, unless I'm mistaken, a bearing angle of 280&#5156; is going north-west, and the question doesn't say what angle the first ship is going on.  I also do not know how to figure out how far apart they are after two hours.   Help would be much appreciated! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725439 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=725439\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two ships leave Liverpool at the same time. One of them travels north-west at an average speed of 10.5 km/h while the other travels at an average speed of 14 km/h on a bearing of 280&#5156;. How far apart are these ships after 2 hours? <BR>\n" );
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document.write( "Exactly northwest is 315 degrees so the angle between the two ship's path is:<BR>\n" );
document.write( "315-280 = 35 degrees<BR>\n" );
document.write( "Find the distance each ship has traveled in two hrs; dist = time * speed<BR>\n" );
document.write( "2*10.5 = 21 km<BR>\n" );
document.write( "and<BR>\n" );
document.write( "2*14 = 28 km<BR>\n" );
document.write( "We have a triangle we can solve; the enclosed angle is 35 degrees (A), has legs of 21 and 28 km. the distance between the ships is the side opposite this angle a<BR>\n" );
document.write( "Use the law of cosines a^2 = b^2 + c^2 - 2(b*c)cos(A)<BR>\n" );
document.write( "In this problem<BR>\n" );
document.write( "a^2 = 21^2 + 28^2 - 2(21*28)Cos(35)<BR>\n" );
document.write( "a^2 = 441 + 784 - 2(588)*.819<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%28271.67%29 ALIGN=MIDDLE  ALT=\"sqrt%28271.67%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 16.17 km apart after two hours<BR>\n" );
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document.write( "this is the method, I'll let you check my math.   </SPAN>\n" );
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