document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970320>Question 970320</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two planes leave an airport at the same time, one flying due west at 500 km/h and the other flying due southeast at 300 km/h. What is the distance between the planes two hours later. What do I do if there is no angle because I have to use trig. Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592968 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> W+++Start<BR>\n" );
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document.write( " ;;;;;;;;;;;;;+SE\r<BR>\n" );
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document.write( "The angle between SE and W is 135 degrees.  SE is half way between E (90) and S (180)\r<BR>\n" );
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document.write( "Two hours later, the plane flying west has gone 1000 km; the one SE 600 km.  If they were in opposite directions, the distance would be 1600 km; the same direction and it would be 400 km, so the answer is between these values and closer to 1600 km by the picture above.\r<BR>\n" );
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document.write( "The angle between them is 135 degrees\r<BR>\n" );
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document.write( "The side you want is c.<BR>\n" );
document.write( "a=1000<BR>\n" );
document.write( "b=600<BR>\n" );
document.write( "the angle between is theta, and it is 135 degrees  cos (135)=-(sqrt(2)/2))\r<BR>\n" );
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document.write( "C^2=a^2 +b^2-2ab cos theta    LAW OF COSINES\r<BR>\n" );
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document.write( "c^2=1000000+360000+2(1000)(600)(.7071) ; .7071 is sqrt (2)/2.  The last term is positive, because the cosine is negative, and there are two negatives.<BR>\n" );
document.write( "c^2=1360000+848520=2208520.\r<BR>\n" );
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document.write( "c=1486.1 miles.  <BR>\n" );
document.write( "This makes intuitive sense.\r<BR>\n" );
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