document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190310>Question 1190310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two poles have wires running from the top of each to the base of the base of the other. If the poles are 8 m and 12 m high, at what height do the wires cross? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821950 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821950\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The answer from the first tutor uses algebra and equations of lines to solve the problem.  That is a valid approach (and you should understand and be able to use it), but it is not very efficient.<br><BR>\n" );
document.write( "The response from the other tutor gives you the right answer; but you learn nothing from it.<br><BR>\n" );
document.write( "If you run into this kind of problem frequently -- e.g., if you compete in timed math competitions -- then this is a handy formula to memorize:<br><BR>\n" );
document.write( "If the heights of the two towers are A and B, then the height where the wires cross is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%2F%28A%2BB%29 ALIGN=MIDDLE  ALT=\"AB%2F%28A%2BB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > -- independent of the distance between the towers.<br><BR>\n" );
document.write( "If you want to LEARN something about that formula, you can derive it using similar triangles.<br><BR>\n" );
document.write( "Here is a diagram....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-2%2C12%2C-2%2C16%0D%0A%2Cline%280%2C0%2C10%2C0%29%2Cline%280%2C0%2C0%2C8%29%2Cline%2810%2C0%2C10%2C12%29%2Cline%280%2C8%2C10%2C0%29%2Cline%280%2C0%2C10%2C12%29%0D%0A%2Cline%284%2C0%2C4%2C4.8%29%0D%0A%2Clocate%28-1%2C-.5%2C%22A%280%2C0%29%22%29%2Clocate%289%2C-.5%2C%22C%2810%2C0%29%22%29%2Clocate%28-1%2C9%2C%22B%280%2C8%29%22%29%2Clocate%289%2C13%2C%22D%2810%2C12%29%22%29%2Clocate+%284%2C6%2CE%29%2Clocate%284%2C-.5%2CF%29%0D%0A%2Clocate%282%2C1%2Cx%29%2Clocate%286%2C1%2C%2210-x%22%29%2Clocate%284.5%2C2.4%2Cy%29%0D%0A%2Clocate%28.5%2C4%2C8%29%2Clocate%289%2C6%2C12%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(1) Triangles CEF and CBA are similar:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EF%2FAB=y%2F8=%2810-x%29%2F10 ALIGN=MIDDLE  ALT=\"EF%2FAB=y%2F8=%2810-x%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) Triangles AEF and ADC are similar:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EF%2FCD=y%2F12=x%2F10 ALIGN=MIDDLE  ALT=\"EF%2FCD=y%2F12=x%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "From (1) and (2),<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F8%2By%2F12=%2810-x%29%2F10%2Bx%2F10=10%2F10=1 ALIGN=MIDDLE  ALT=\"y%2F8%2By%2F12=%2810-x%29%2F10%2Bx%2F10=10%2F10=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve for y:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F8%2By%2F12=1 ALIGN=MIDDLE  ALT=\"y%2F8%2By%2F12=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply by the common denominator, without simplifying:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y%2B8y=12%2A8 ALIGN=MIDDLE  ALT=\"12y%2B8y=12%2A8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2812%2B8%29=12%2A8 ALIGN=MIDDLE  ALT=\"y%2812%2B8%29=12%2A8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2812%2A8%29%2F%2812%2B8%29 ALIGN=MIDDLE  ALT=\"y=%2812%2A8%29%2F%2812%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );