document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=273868>Question 273868</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the tow wires cross.\r<BR>\n" );
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document.write( "Find x, the distance from C to the taller pole?\r<BR>\n" );
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document.write( "How high above the ground is the coupling?\r<BR>\n" );
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document.write( "How far down the wire from the smaller pole is the coupling?\r<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 #366473 by </B><A HREF=/tutors/aboutme.mpl?userid=noelsanoj><B>noelsanoj(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=noelsanoj><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=noelsanoj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=366473\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A be the distance from the ground to the coupling C (perpendicular to the ground and parallel to both poles)<BR>\n" );
document.write( "Let D be the distance from the tallest poll to the point on the ground from C.\r<BR>\n" );
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document.write( "(Angle-Angle (AA) Similarity) two pair of similar triangles are formed.<BR>\n" );
document.write( "Using proportions on the smaller pair of triangles to find the distance on the ground from under C to the largest pole.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2830%2F40%29+=+%28a%2Fd%29 ALIGN=MIDDLE  ALT=\"%2830%2F40%29+=+%28a%2Fd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "30d = 40a<BR>\n" );
document.write( "for the larger pair of triangles<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850%2F40%29+=+%28a%2F40-d%29 ALIGN=MIDDLE  ALT=\"%2850%2F40%29+=+%28a%2F40-d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "50(40-d) = 40a\r<BR>\n" );
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document.write( "Notice 40a, substituting on both equations<BR>\n" );
document.write( "30d)=50(40-d)<BR>\n" );
document.write( "30a = 2000-50d<BR>\n" );
document.write( "80d = 2000<BR>\n" );
document.write( "d = 25 feet. If you subtract from 40 you get the other base which is 15ft.\r<BR>\n" );
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document.write( "Substitute to find the height of the coupling<BR>\n" );
document.write( "30d = 40a<BR>\n" );
document.write( "30(25)=40a<BR>\n" );
document.write( "a=750/40<BR>\n" );
document.write( "a=18.75 feet height.\r<BR>\n" );
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document.write( "How far down the wire from the smaller pole is the coupling?<BR>\n" );
document.write( "Notice that the smaller pole formed a dilation by a factor 10 from a 3,4,5 triangle. Therefore, the wire from the smaller pole to the base of the larger is 50ft. Then using the Triangle Proportionality Theorem, formulate the following proportion. <BR>\n" );
document.write( "Let y be the distance of the segment from the pole to C (Coupling) use the proportion.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F15=50%2F40 ALIGN=MIDDLE  ALT=\"y%2F15=50%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28750%2F40%29 ALIGN=MIDDLE  ALT=\"y=%28750%2F40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y=18.75 feet<BR>\n" );
document.write( "For the distance from C to the Taller pole, using Pythagoras <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=50%5E2%2B40%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=50%5E2%2B40%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > the hypotenuse is about 64 feet round to the unit.\r<BR>\n" );
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document.write( "To find the distance from C to the taller pole, again use the Triangle Proportionality Theorem..<BR>\n" );
document.write( "Let p be the distance from C to the Taller pole.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2F25=64%2F40 ALIGN=MIDDLE  ALT=\"p%2F25=64%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The distance is 40 feet. </SPAN>\n" );
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