document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147781>Question 147781</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. A bell rope, passing through the ceiling above, just barely reaches the belfry floor. When one pulls the rope to the wall, keeping the rope taut, it reaches a point that is three inches above the floor. It is four feet from the wall to the rope when the rope is hanging freely. How high is the ceiling? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108157 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=108157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First draw a straight line from the top of the tower to the floor. Denote the length as \"x\":\r<BR>\n" );
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document.write( "Now pull back the rope, this will angle the rope\r<BR>\n" );
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document.write( "Draw a triangle between the endpoint of the drawn rope to the rope's resting position. Since the horizontal length between the resting position and the new position is 4 feet (48 inches) be sure to draw that in:\r<BR>\n" );
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document.write( "Now draw a rectangle right underneath the triangle like this. Take note that the height of this rectangle is 3 inches. Also, notice how the vertical leg of the triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3 ALIGN=MIDDLE  ALT=\"x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches (subtract the height 3 from the rope length x to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3 ALIGN=MIDDLE  ALT=\"x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches):\r<BR>\n" );
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document.write( "So we now have a triangle. We can use Pythagorean's Theorem to find the length of the rope (which is the hypotenuse)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with Pythagorean's Theorem\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2B48%5E2=x%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2B48%5E2=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=x-3 ALIGN=MIDDLE  ALT=\"a=x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the length of the vertical leg), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=48 ALIGN=MIDDLE  ALT=\"b=48\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the length of the horizontal leg), and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=x ALIGN=MIDDLE  ALT=\"c=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2B2304=x%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2B2304=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 48 to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9%2B2304=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9%2B2304=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%2B9%2B2304=0 ALIGN=MIDDLE  ALT=\"-6x%2B9%2B2304=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%2B2313=0 ALIGN=MIDDLE  ALT=\"-6x%2B2313=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x=0-2313 ALIGN=MIDDLE  ALT=\"-6x=0-2313\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2313 ALIGN=MIDDLE  ALT=\"2313\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x=-2313 ALIGN=MIDDLE  ALT=\"-6x=-2313\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2313%29%2F%28-6%29 ALIGN=MIDDLE  ALT=\"x=%28-2313%29%2F%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=771%2F2 ALIGN=MIDDLE  ALT=\"x=771%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=771%2F2 ALIGN=MIDDLE  ALT=\"x=771%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Which approximates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=385.5 ALIGN=MIDDLE  ALT=\"x=385.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So the length of the rope (and the consequently the height of the ceiling) is 385.5 inches which is 32 1/8 feet or 32 feet 1 and a half inches.<BR>\n" );
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