document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=568999>Question 568999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two vertical poles have heights 6 ft. and 12 ft. A rope is stretched from the top of each poles to the bottom of the other. How far above the ground do the ropes cross? <BR>\n" );
document.write( "*Note: I need to solve this problem using similar triangles. <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367339 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=367339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C240%2C-12%2C6%2C-1.5%2C13.5%2C%0D%0Atriangle%28-10%2C0%2C-10%2C12%2C0%2C4%29%2C%0D%0Atriangle%280%2C4%2C5%2C0%2C5%2C6%29%2C%0D%0Aline%280%2C0%2C0%2C4%29%2C+line%28-12%2C0%2C6%2C0%29%2C%0D%0Alocate%28-10.2%2C0%2CA%29%2C+locate%28-0.2%2C0%2CF%29%2Clocate%284.8%2C0%2CE%29%2C%0D%0Alocate%28-10.2%2C13%2CB%29%2C+locate%28-0.2%2C5%2CC%29%2Clocate%284.8%2C7%2CD%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > AB and ED are the poles (perfectly vertical). BE and DA are the ropes that cross at C.<BR>\n" );
document.write( "F is the point directly below C on the ground (line AE), which is pefrectly flat and horizontal.<BR>\n" );
document.write( "The vertical poles are part of parallel lines.<BR>\n" );
document.write( "As a consequence, triangles ABC and DEC have congruent angles at B and E, and at A and D (alternate interior). Of course, ABC and DEC also have congruent angles at C (vertical angles).<BR>\n" );
document.write( "Triangles ABC and DEC are similar, with corresponding sides in the ratio 2:1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%2FDE=BC%2FEC=AC%2FDC=2%2F1 ALIGN=MIDDLE  ALT=\"AB%2FDE=BC%2FEC=AC%2FDC=2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In particular,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=2EC ALIGN=MIDDLE  ALT=\"BC=2EC\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BE=BC%2BEC=2EC%2BEC=3EC ALIGN=MIDDLE  ALT=\"BE=BC%2BEC=2EC%2BEC=3EC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Right triangles ABE and FCE, with the same angle at E, are also similar, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%2FFC=BE%2FCE=3EC%2FEC3%2F1 ALIGN=MIDDLE  ALT=\"AB%2FFC=BE%2FCE=3EC%2FEC3%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=3FC ALIGN=MIDDLE  ALT=\"AB=3FC\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FC=AB%2F3=12ft%2F3=highlight%284ft%29 ALIGN=MIDDLE  ALT=\"FC=AB%2F3=12ft%2F3=highlight%284ft%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The ropes cross 4 ft above the ground. </SPAN>\n" );
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