document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=43142>Question 43142</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two planes leave an airport at the same time, one flying due west at 500km/h and the other flying due southeast at 300km/h. What is the distance between the planes two hours later? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #28175 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=28175\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: Distance = Speed x Time\r<BR>\n" );
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document.write( "In 2 hours, the plane travelling to West travels a distance of 500x2 = 1000 km.<BR>\n" );
document.write( "In 2 hours, the plane travelling to South-East travels a distance of 300x2 = 600 km.\r<BR>\n" );
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document.write( "If their initial position was the point O then their final positions, after 2 hours, are points A and B respectively.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-110%2C110%2C-110%2C110%2C%0D%0Aline%280%2C0%2C42.4264%2C-42.4264%29%2C%0D%0Aline%280%2C0%2C-100%2C0%29%2C%0D%0Aline%2842.4264%2C-42.4264%2C-100%2C0%29%2C%0D%0Alocate%280%2C-1%2CO%29%2C%0D%0Alocate%28-100%2C0%2CA%29%2C%0D%0Alocate%2842.4264%2C-42.4264%2CB%29%2C%0D%0Ablue%28arrow%280%2C50%2C0%2C75%29%2Carrow%280%2C50%2C25%2C50%29%2Carrow%280%2C50%2C-25%2C50%29%2Carrow%280%2C50%2C0%2C25%29%29%2C%0D%0Alocate%2826%2C50%2CE%29%2C%0D%0Alocate%281%2C75%2CN%29%2C%0D%0Alocate%28-26%2C50%2CW%29%2C%0D%0Alocate%281%2C25%2CS%29%2C%0D%0Aline%2842.4264%2C-42.4264%2C42.4264%2C0%29%2C%0D%0Aline%2842.4264%2C0%2C0%2C0%29%2C%0D%0Alocate%2843.4264%2C1%2CC%29%2C%0D%0Alocate%28-50%2C8%2C1000%29%2C%0D%0Alocate%2815%2C-23%2C600%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We need to know the length of AB.<BR>\n" );
document.write( "In triangle BCO, <BCO is right angle and <BOC = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%5Eo ALIGN=MIDDLE  ALT=\"45%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > as OB is in South-East direction.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OC%2FOB ALIGN=MIDDLE  ALT=\"OC%2FOB\"   DISABLED_style= \"max-width:90%; height:auto;\" > = cos(< BOC) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2845%5Eo%29 ALIGN=MIDDLE  ALT=\"cos%2845%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OC%2F600+=+cos%2845%5Eo%29 ALIGN=MIDDLE  ALT=\"OC%2F600+=+cos%2845%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OC%2F600+=+1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"OC%2F600+=+1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OC+=+600%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"OC+=+600%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OC+=+300sqrt%282%29 ALIGN=MIDDLE  ALT=\"OC+=+300sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "or OC = 424.264 km\r<BR>\n" );
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document.write( "Therefore, AC = AO + OC = 1000 + 424.264 = 1424.264 km\r<BR>\n" );
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document.write( "As BCO is a right angled isosceles triangle with <BCO as right angle, so OC = BC. Hence BC = 424.264 km.\r<BR>\n" );
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document.write( "Now, in triangle ACB, <ACB is right angle.<BR>\n" );
document.write( "Applying Pythagorus theorem,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%5E2+=+AC%5E2+%2B+BC%5E2 ALIGN=MIDDLE  ALT=\"AB%5E2+=+AC%5E2+%2B+BC%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%5E2+=+1424.264%5E2+%2B+424.264%5E2 ALIGN=MIDDLE  ALT=\"AB%5E2+=+1424.264%5E2+%2B+424.264%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%5E2+=+2208528.14 ALIGN=MIDDLE  ALT=\"AB%5E2+=+2208528.14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB+=+sqrt%282208528.14%29 ALIGN=MIDDLE  ALT=\"AB+=+sqrt%282208528.14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or AB = 1486.112 km\r<BR>\n" );
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document.write( "Hence, the reqd. distance between the two planes after 2 hours is 1486.112 km. </SPAN>\n" );
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