document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42890>Question 42890</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072538953/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A guy wire of length 50 feet is attached to the ground and to the top of an antenna.  The height of the antenna is 10 feet larger than the distance from the base of the antenna to the point where the guy wire is attached to the ground.  What is the height of the antenna? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27978 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-10%2C50%2C-10%2C50%2C%0D%0Arectangle%280%2C0%2C2%2C40%29%2C%0D%0Aline%282%2C40%2C30%2C0%29%2C%0D%0Aline%28-5%2C0%2C35%2C0%29%2C%0D%0Alocate%283%2C40%2CA%29%2C%0D%0Alocate%2830.5%2C0%2CC%29%2C%0D%0Alocate%282.5%2C0%2CB%29%2C%0D%0Alocate%28-7%2C20%2CANTENNA%29%2C%0D%0Alocate%2818%2C20%2CWIRE%29%2C%0D%0Alocate%2820%2C-1%2CGROUND%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Considering triangle ABC, <ABC is a right angle.<BR>\n" );
document.write( "So we can apply Pythagorus theorem: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Hypotanuse%5E2+=+Base%5E2+%2B+Height%5E2 ALIGN=MIDDLE  ALT=\"Hypotanuse%5E2+=+Base%5E2+%2B+Height%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here base = BC, height = AB and hypotanuse = AC.\r<BR>\n" );
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document.write( "Given: AC = 50 ft.<BR>\n" );
document.write( "Let BC = x feet. <BR>\n" );
document.write( "Then, AB = (x+10) feet \r<BR>\n" );
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document.write( "[This is because height of the antenna is 10 ft larger than the distance from the base of the antenna to the point where the guy wire is attached to the ground].\r<BR>\n" );
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document.write( "So from Pythagorus theorem we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%5E2+=+x%5E2+%2B+%28x%2B10%29%5E2 ALIGN=MIDDLE  ALT=\"50%5E2+=+x%5E2+%2B+%28x%2B10%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%5E2+=+x%5E2+%2B+x%5E2+%2B+20x+%2B+10%5E2 ALIGN=MIDDLE  ALT=\"50%5E2+=+x%5E2+%2B+x%5E2+%2B+20x+%2B+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+20x+%2B+10%5E2+-+50%5E2+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+20x+%2B+10%5E2+-+50%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+20x+%2B+100+-+2500+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+20x+%2B+100+-+2500+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+20x+-+2400+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+20x+-+2400+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+10x+-+1200+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+10x+-+1200+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+40x+-+30x+-+1200+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+40x+-+30x+-+1200+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x+%2B+40%29+-+30%28x+%2B+40%29+=+0 ALIGN=MIDDLE  ALT=\"x%28x+%2B+40%29+-+30%28x+%2B+40%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B40%29%28x-30%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B40%29%28x-30%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So either (x + 40) = 0 or (x - 30) = 0 i.e. either x = -40 or x = 30.<BR>\n" );
document.write( "Now, 'x' being the length of a side of a triangle cannot be negative.\r<BR>\n" );
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document.write( "So x = 30 i.e. the distance of the base of the antenna from the point where the guy wire is attached to the ground is 30 feet.\r<BR>\n" );
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document.write( "Hence, the height of the antenna is (x+10) = 30+10 = 40 feet. </SPAN>\n" );
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