document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=874044>Question 874044</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help please.<BR>\n" );
document.write( "A foot tall tree casts a shadow that is one foot shorter than the distance from the tip of the shadow to the top of the tree. Find the length of shadow.<BR>\n" );
document.write( "(a) Let x represent the length of the shadow. Write an expression for the diagonal distance from the tip of the shadow to the top of the tree.<BR>\n" );
document.write( "(B) What is the length of the shadow? (Hint use the pythagorean formula) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #527414 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=527414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Is it a 1-foot tall tree?<BR>\n" );
document.write( "Is it an h-foot tall tree?<BR>\n" );
document.write( "How tall is that tree?<BR>\n" );
document.write( "If you do not have a number for the tree's height,<BR>\n" );
document.write( "it gets a little more complicated.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If the height of the tree (in feet) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the length of the shadow in feet, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the diagonal distance from the tip of the shadow to the top of the tree, in feet,<BR>\n" );
document.write( "and it is like this (drawing not to scale, lengths in feet):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C250%2C-5%2C1%2C-1%2C4%2C%0D%0Atriangle%280%2C0%2C0%2C3%2C-4%2C0%29%2C%0D%0Arectangle%280%2C0%2C-0.2%2C0.2%29%2C%0D%0Arectangle%280%2C0%2C0.1%2C0.5%29%2C%0D%0Agreen%28triangle%28-0.5%2C0.5%2C0.52%2C0.5%2C0%2C3%29%29%2C%0D%0Alocate%280.05%2C1.7%2Ch%29%2Clocate%28-2.1%2C-0.01%2Cx%29%2C%0D%0Alocate%28-2.1%2C1.5%2Cx%2B1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2=x%5E2%2Bh%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2=x%5E2%2Bh%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=sqrt%28x%5E2%2Bh%5E2%29 ALIGN=MIDDLE  ALT=\"x%2B1=sqrt%28x%5E2%2Bh%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "If you do not know the height of the tree, all you can get is formulas to calculate those distances.<BR>\n" );
document.write( "In that case,<BR>\n" );
document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=sqrt%28x%5E2%2Bh%5E2%29 ALIGN=MIDDLE  ALT=\"x%2B1=sqrt%28x%5E2%2Bh%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the diagonal distance from the tip of the shadow to the top of the tree, in feet,<BR>\n" );
document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2=x%5E2%2Bh%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2=x%5E2%2Bh%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B1=x%5E2%2Bh%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B1=x%5E2%2Bh%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1=h%5E2 ALIGN=MIDDLE  ALT=\"2x%2B1=h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=h%5E2-1 ALIGN=MIDDLE  ALT=\"2x=h%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28h%5E2-1%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28h%5E2-1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the length of the shadow.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If you knew the height of the tree,<BR>\n" );
document.write( "you could substitute the value sooner rather than later,<BR>\n" );
document.write( "and the algebra would get easier.<BR>\n" );
document.write( "For example for a 3-foot tall tree, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3 ALIGN=MIDDLE  ALT=\"h=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2=x%5E2%2B3%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2=x%5E2%2B3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2=x%5E2%2B9 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2=x%5E2%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=sqrt%28x%5E2%2B9%29 ALIGN=MIDDLE  ALT=\"x%2B1=sqrt%28x%5E2%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > we write<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2=x%5E2%2B9 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2=x%5E2%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B1=x%5E2%2B9 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B1=x%5E2%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1=9 ALIGN=MIDDLE  ALT=\"2x%2B1=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=9-1 ALIGN=MIDDLE  ALT=\"2x=9-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=8 ALIGN=MIDDLE  ALT=\"2x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8%2F2 ALIGN=MIDDLE  ALT=\"x=8%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "For a 5-foot tall tree, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=5 ALIGN=MIDDLE  ALT=\"h=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2=x%5E2%2B5%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2=x%5E2%2B5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2=x%5E2%2B25 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2=x%5E2%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%2B1=sqrt%28x%5E2%2B25%29%29 ALIGN=MIDDLE  ALT=\"highlight%28x%2B1=sqrt%28x%5E2%2B25%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is \"an expression for the diagonal distance from the tip of the shadow to the top of the tree.\"<BR>\n" );
document.write( "B) To solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the length of the shadow in feet) we write<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2=x%5E2%2B25 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2=x%5E2%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B1=x%5E2%2B25 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B1=x%5E2%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1=25 ALIGN=MIDDLE  ALT=\"2x%2B1=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=25-1 ALIGN=MIDDLE  ALT=\"2x=25-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=24 ALIGN=MIDDLE  ALT=\"2x=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=24%2F2 ALIGN=MIDDLE  ALT=\"x=24%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=12%29 ALIGN=MIDDLE  ALT=\"highlight%28x=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The length of the shadow is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x12%29 ALIGN=MIDDLE  ALT=\"highlight%28x12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );