document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112637>Question 1112637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boulder stops a surveyor from directly measuring the boundary AB of a piece of land. He measures AC=500 feet and extends it 10 feet to a point D. BC turns out to be 600 feet and extending it 12 feet to reach point E. What is the length of AB if ED is 8 feet? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #727698 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=727698\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sketch below (not to scale) illustrates the situation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C450%2C-5%2C17%2C-1.5%2C31.5%2C%0D%0Atriangle%280%2C0%2C2.5%2C19.843%2C16%2C0%29%2C%0D%0Atriangle%28-4.25%2C29.765%2C2.5%2C19.843%2C3.75%2C29.765%29%2C%0D%0Alocate%28-0.6%2C0%2CA%29%2Clocate%2815.8%2C0%2CB%29%2C%0D%0Alocate%282.7%2C20.5%2CC%29%2Clocate%283.5%2C30.9%2CD%29%2C%0D%0Alocate%28-4.4%2C30.9%2CE%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The sketch is purposely not to scale, because triangle DEC is so small compared to triangle ABC, that making DEC to scale would make it almost invisible.<BR>\n" );
document.write( "Triangles ABC and DEC must have been designed by the surveyor<BR>\n" );
document.write( "so as to be similar triangles.<BR>\n" );
document.write( "Their angles at C are congruent because they are vertical angles.<BR>\n" );
document.write( "sides EC and DC were made to be proportional to BC  and AC respectively:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%2FEC=600ft%2F%2212+ft%22=50 ALIGN=MIDDLE  ALT=\"BC%2FEC=600ft%2F%2212+ft%22=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC%2FDC=500ft%2F%2210+ft%22=50 ALIGN=MIDDLE  ALT=\"AC%2FDC=500ft%2F%2210+ft%22=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Because there is obe pair of congruent angles at C,<BR>\n" );
document.write( "flanked by pairs of proportional sides,<BR>\n" );
document.write( "triangles ABC and DEC are similar triangles \"by SAS similarity\".<BR>\n" );
document.write( "DEC is a scale down version of ABC,<BR>\n" );
document.write( "with all lengths in  ABC being <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > times greater.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%2FED=50 ALIGN=MIDDLE  ALT=\"AB%2FED=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%2F%228+ft%22=50 ALIGN=MIDDLE  ALT=\"AB%2F%228+ft%22=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=50%288ft%29 ALIGN=MIDDLE  ALT=\"AB=50%288ft%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28AB=400ft%29 ALIGN=MIDDLE  ALT=\"highlight%28AB=400ft%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );