document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135793>Question 1135793</A>: <I><SPAN STYLE=\"word-break: break-all;\">  In a circular tent, the last row of seats are to be placed 75-feet away from a central pole that is 56-feet high. Ropes from the top of the pole are to be staked into the ground in such a way that they are 6-feet above ground where the last row of seats are to be placed. At what distance from the central pole should the ropes be staked in? Please round to one decimal place.<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 #753467 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=753467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "Answer: <font size=4 color=red>84 feet</font>\r<BR>\n" );
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document.write( "Explanation on how to get that answer:\r<BR>\n" );
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document.write( "Draw out the diagram. Technically this isn't needed but it's handy for visual learners (such as myself).<BR>\n" );
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document.write( "Point A = base of the pole<BR>\n" );
document.write( "Point B = top of the pole<BR>\n" );
document.write( "Point C = base of the seats in the last row<BR>\n" );
document.write( "Point D = highest point just above point C (aka the ceiling over the last row)<BR>\n" );
document.write( "Point E = location where the rope is staked into the ground\r<BR>\n" );
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document.write( "As you can see, we have two similar triangles: Triangle ABE and triangle CDE<BR>\n" );
document.write( "They can be proven similar by the AA (angle angle) similarity theorem. \r<BR>\n" );
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document.write( "Based on the points mentioned, we can say these facts<BR>\n" );
document.write( "<ul><li>AB = 56 = the height of the pole</li><li>AC = 75 = distance from the base of the pole to the base of the stands in the last row</li><li>CD = 6 = clearance height for people in the last row</li><li>CE = x =  distance from the base of the stands in the last row to where the rope is staked in the ground</li></ul>\r<BR>\n" );
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document.write( "Furthermore, we know that<BR>\n" );
document.write( "AE = AC + CE<BR>\n" );
document.write( "AE = 75 + x<BR>\n" );
document.write( "based on the segment addition postulate\r<BR>\n" );
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document.write( "Now use the idea that the triangles are similar to set up a proportion. Then cross multiply to solve for x<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2856%29%2F%286%29+=+%2875%2Bx%29%2F%28x%29 ALIGN=MIDDLE  ALT=\"%2856%29%2F%286%29+=+%2875%2Bx%29%2F%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitution\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56x+=+6%2875%2Bx%29 ALIGN=MIDDLE  ALT=\"56x+=+6%2875%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56x+=+6%2875%29%2B6%28x%29 ALIGN=MIDDLE  ALT=\"56x+=+6%2875%29%2B6%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56x+=+450%2B6x ALIGN=MIDDLE  ALT=\"56x+=+450%2B6x\"   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=56x-6x+=+450%2B6x-6x ALIGN=MIDDLE  ALT=\"56x-6x+=+450%2B6x-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 6x from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50x+=+450 ALIGN=MIDDLE  ALT=\"50x+=+450\"   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=%2850x%29%2F50+=+450%2F50 ALIGN=MIDDLE  ALT=\"%2850x%29%2F50+=+450%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 50\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+9 ALIGN=MIDDLE  ALT=\"x+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means CE = 9 and<BR>\n" );
document.write( "AE = AC + CE<BR>\n" );
document.write( "AE = 75 + x<BR>\n" );
document.write( "AE = 75 + 9<BR>\n" );
document.write( "AE = 84<BR>\n" );
document.write( "which is the distance we want: the distance from the base of the pole to where the rope is staked into the ground. <BR>\n" );
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