document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147777>Question 147777</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 #108146 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=108146\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First let's draw out the problem\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/tower_1.jpg\" alt=\"Photobucket - Video and Image Hosting\"><br><br>\r<BR>\n" );
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document.write( "Now take the triangle and make a mirror copy like this:\r<BR>\n" );
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document.write( "Now draw a curve from either endpoint like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/tower_3.jpg\" alt=\"Photobucket - Video and Image Hosting\"><br><br>\r<BR>\n" );
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document.write( "Notice how a circular sector is formed. If we take the rope and swing it 360 degrees, it will form a circle where the rope is the radius. \r<BR>\n" );
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document.write( "Also, if we add the 2 lengths 4 feet and 4 feet to get 8 feet or 96 inches, this forms a chord on the circle. Furthermore, the length 3 inches forms the sagitta of the circle (ie the length that is perpendicular to a chord). \r<BR>\n" );
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document.write( "Now it turns out that if we know the length of a chord of a circle and its corresponding sagitta, then we can find the radius of the circle. The radius can be found through the formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%28c%5E2%29%2F%288s%29%2Bs%2F2 ALIGN=MIDDLE  ALT=\"r=%28c%5E2%29%2F%288s%29%2Bs%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where \"c\" is the length of the chord and \"s\" is the length of the sagitta.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%28c%5E2%29%2F%288s%29%2Bs%2F2 ALIGN=MIDDLE  ALT=\"r=%28c%5E2%29%2F%288s%29%2Bs%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%2896%5E2%29%2F%288%2A3%29%2B3%2F2 ALIGN=MIDDLE  ALT=\"r=%2896%5E2%29%2F%288%2A3%29%2B3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=96 ALIGN=MIDDLE  ALT=\"c=96\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=3 ALIGN=MIDDLE  ALT=\"s=3\"   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=r=%289216%29%2F%288%2A3%29%2B3%2F2 ALIGN=MIDDLE  ALT=\"r=%289216%29%2F%288%2A3%29%2B3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 96 to get 9,216\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%289216%29%2F%2824%29%2B3%2F2 ALIGN=MIDDLE  ALT=\"r=%289216%29%2F%2824%29%2B3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=771%2F2 ALIGN=MIDDLE  ALT=\"r=771%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions and simplify\r<BR>\n" );
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document.write( "So the radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=385.5 ALIGN=MIDDLE  ALT=\"r=385.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the length of the rope is 385.5 inches or 32 feet 1 and half inches. Since the rope \"barely reaches the belfry floor\", this means that the length of the rope and the height of the ceiling are really close. So we can say that the height of the ceiling is approximately 385.5 inches or 32 feet 1 and half inches. \r<BR>\n" );
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