document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=855629>Question 855629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help me solve this problem please\r<BR>\n" );
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document.write( "A six foot man is standing atop a 9 foot wall. The distance along the hypotenuse from the top of the man's head to the ground is 17 feet. Kneeling children are lined up at the base of the wall. Each kneeling child takes up 1 foot of horizontal space. How many children can kneel along the bottom of the triangle? Assume the wall and the man are vertical, forming a right trial with the ground. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515508 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=515508\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This looks like the first part of a 3-part problem asked as question 855638, question 855639, and question 855640.<BR>\n" );
document.write( "Here is a copy of my previous answer.<BR>\n" );
document.write( " <BR>\n" );
document.write( "a) A 6 foot man is standing atop a 9 foot wall The distance along the hypotenuse from the top of the man's head to the ground is 17 feet. Kneeling children are lined up at the base of the wall. Each kneeling child takes up 1 foot of horizontal space.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C300%2C-9.5%2C2.5%2C-1.5%2C16.5%2C%0D%0Atriangle%28-15%2C0%2C5%2C0%2C-4%2C-20%29%2Cgreen%28rectangle%280%2C0%2C-0.4%2C0.4%29%29%2C%0D%0Arectangle%280%2C0%2C1.5%2C9%29%2Clocate%28-4%2C7.5%2Cgreen%2817%29%29%2C%0D%0Alocate%28-1%2C7.5%2Cgreen%2815%29%29%2Clocate%28-4.2%2C1.5%2Cgreen%28x%29%29%2C%0D%0Acircle%280.1%2C14.7%2C0.3%29%2Cline%280.1%2C14.3%2C1%2C9%29%2C%0D%0Aline%280.2%2C9%2C0.5%2C12%29%2Cgreen%28triangle%28-8%2C0%2C0%2C0%2C0%2C15%29%29%2C%0D%0Aarc%28-5.5%2C0%2C1%2C1.5%2C180%2C360%29%2Carc%28-6.5%2C0%2C1%2C1.5%2C180%2C360%29%2Carc%28-7.5%2C0%2C1%2C1.5%2C180%2C360%29%2C%0D%0Aarc%28-0.5%2C0%2C1%2C1.5%2C180%2C360%29%2Carc%28-1.5%2C0%2C1%2C1.5%2C180%2C360%29%2Carc%28-2.5%2C0%2C1%2C1.5%2C180%2C360%29%2C%0D%0Aarc%28-3.5%2C0%2C1%2C1.5%2C180%2C360%29%2Carc%28-4.5%2C0%2C1%2C1.5%2C180%2C360%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > There is a green right triangle with leg measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet, and hypotenuse measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17 ALIGN=MIDDLE  ALT=\"17\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet.<BR>\n" );
document.write( "According to the Pythagorean theorem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B15%5E2=17%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B15%5E2=17%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B225=289 ALIGN=MIDDLE  ALT=\"x%5E2%2B225=289\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=289-225 ALIGN=MIDDLE  ALT=\"x%5E2=289-225\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=64 ALIGN=MIDDLE  ALT=\"x%5E2=64\"   DISABLED_style= \"max-width:90%; height:auto;\" >--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%2864%29 ALIGN=MIDDLE  ALT=\"x=sqrt%2864%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=8%29 ALIGN=MIDDLE  ALT=\"highlight%28x=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The horizontal space along the bottom of the triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=8%29 ALIGN=MIDDLE  ALT=\"highlight%28x=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%288%29 ALIGN=MIDDLE  ALT=\"highlight%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > kneeling children (each one taking up 1 foot of horizontal space fit on that leg of the right triangle.<BR>\n" );
document.write( " <BR>\n" );
document.write( "b)The man jumps off the original wall and 4 children are removed from the left side of the line. A new triangle is formed. What is the length of the hypotenuse of the new triangle measured from the top of the wall to the ground?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C300%2C-9.5%2C2.5%2C-1.5%2C16.5%2C%0D%0Atriangle%28-15%2C0%2C5%2C0%2C-4%2C-20%29%2Cgreen%28rectangle%280%2C0%2C-0.4%2C0.4%29%29%2C%0D%0Arectangle%280%2C0%2C1.5%2C9%29%2Clocate%28-2%2C4.5%2Cgreen%28y%29%29%2C%0D%0Alocate%28-0.5%2C4.5%2Cgreen%289%29%29%2Clocate%28-2.2%2C1.5%2Cgreen%284%29%29%2C%0D%0Acircle%28-7.9%2C5.7%2C0.3%29%2Cline%28-7.9%2C5.3%2C-8%2C0%29%2C%0D%0Aline%28-7.8%2C3%2C-7.5%2C0%29%2Cgreen%28triangle%28-4%2C0%2C0%2C0%2C0%2C9%29%29%2C%0D%0Aarc%28-0.5%2C0%2C1%2C1.5%2C180%2C360%29%2Carc%28-1.5%2C0%2C1%2C1.5%2C180%2C360%29%2Carc%28-2.5%2C0%2C1%2C1.5%2C180%2C360%29%2C%0D%0Aarc%28-3.5%2C0%2C1%2C1.5%2C180%2C360%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-4=4 ALIGN=MIDDLE  ALT=\"8-4=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > children left, the horizontal leg of the new right triangle measures only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4feet ALIGN=MIDDLE  ALT=\"4feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The vertical lefg measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+feet ALIGN=MIDDLE  ALT=\"9+feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the height of the wall.<BR>\n" );
document.write( "The Pythagorean realation for the length in feet is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=4%5E2%2B9%5E2 ALIGN=MIDDLE  ALT=\"y%5E2=4%5E2%2B9%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=16%2B81 ALIGN=MIDDLE  ALT=\"y%5E2=16%2B81\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=97 ALIGN=MIDDLE  ALT=\"y%5E2=97\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%2897%29=9.85 ALIGN=MIDDLE  ALT=\"y=sqrt%2897%29=9.85\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded).<BR>\n" );
document.write( "The length of the hypotenuse of the new triangle is approximately<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%289.85feet=9feet10inches%29 ALIGN=MIDDLE  ALT=\"highlight%289.85feet=9feet10inches%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "c) Each child on the ground (from the original triangle in part a) lies down head to toe, taking up 3 feet each. The 6 foot man is still standing on top of the wall, but the wall is shorter now. If the distance along the hypotenuse from the top of the man's head to the ground is exactly 26 feet, what is the new exact height of the wall? <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C300%2C-27%2C3%2C-4%2C14%2C%0D%0Atriangle%28-35%2C0%2C5%2C0%2C-4%2C-20%29%2Cgreen%28rectangle%280%2C0%2C-0.5%2C0.5%29%29%2C%0D%0Arectangle%280%2C0%2C1.5%2C4%29%2Clocate%28-12%2C5%2Cgreen%2826%29%29%2C%0D%0Alocate%28-2%2C5.5%2Cgreen%286%2Bw%29%29%2Clocate%28-11.5%2C1.1%2Cgreen%2824%29%29%2C%0D%0Acircle%280.1%2C9.7%2C0.3%29%2Cline%280.1%2C9.3%2C1%2C4%29%2C%0D%0Aline%280.2%2C4%2C0.5%2C7%29%2Cgreen%28triangle%28-24%2C0%2C0%2C0%2C0%2C10%29%29%2C%0D%0Acircle%28-2.8%2C0.22%2C0.2%29%2Ccircle%28-5.8%2C0.22%2C0.2%29%2Ccircle%28-8.8%2C0.22%2C0.2%29%2C%0D%0Acircle%28-11.8%2C0.22%2C0.2%29%2Ccircle%28-14.8%2C0.22%2C0.2%29%2Ccircle%28-17.8%2C0.22%2C0.2%29%2C%0D%0Acircle%28-20.8%2C0.22%2C0.2%29%2Ccircle%28-23.8%2C0.22%2C0.2%29%2C%0D%0Aline%28-2.8%2C0.03%2C-0.02%2C0.03%29%2Cline%28-0.02%2C0.4%2C-0.02%2C0.03%29%2C%0D%0Aline%28-5.8%2C0.03%2C-3.02%2C0.03%29%2Cline%28-3.02%2C0.4%2C-3.02%2C0.03%29%2C%0D%0Aline%28-8.8%2C0.03%2C-6.02%2C0.03%29%2Cline%28-6.02%2C0.4%2C-6.02%2C0.03%29%2C%0D%0Aline%28-11.8%2C0.03%2C-9.02%2C0.03%29%2Cline%28-9.02%2C0.4%2C-9.02%2C0.03%29%2C%0D%0Aline%28-14.8%2C0.03%2C-12.02%2C0.03%29%2Cline%28-12.02%2C0.4%2C-12.02%2C0.03%29%2C%0D%0Aline%28-17.8%2C0.03%2C-15.02%2C0.03%29%2Cline%28-15.02%2C0.4%2C-15.02%2C0.03%29%2C%0D%0Aline%28-20.8%2C0.03%2C-18.02%2C0.03%29%2Cline%28-18.02%2C0.4%2C-18.02%2C0.03%29%2C%0D%0Aline%28-23.8%2C0.03%2C-21.02%2C0.03%29%2Cline%28-21.02%2C0.4%2C-21.02%2C0.03%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The horizontal leg measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A3=24 ALIGN=MIDDLE  ALT=\"8%2A3=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft and the hypotenuse measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26 ALIGN=MIDDLE  ALT=\"26\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%7D%7D+is+the+new+height+of+the+wall+%28in+feet%29%2C+the+vertical+leg+measures+%7B%7B%7B6%2Bw ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >ft.<BR>\n" );
document.write( "According to the Pythagorean theorem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2Bw%29%5E2%2B24%5E2=26%5E2 ALIGN=MIDDLE  ALT=\"%286%2Bw%29%5E2%2B24%5E2=26%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2Bw%29%5E2%2B576=676 ALIGN=MIDDLE  ALT=\"%286%2Bw%29%5E2%2B576=676\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2Bw%29%5E2=674-576 ALIGN=MIDDLE  ALT=\"%286%2Bw%29%5E2=674-576\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2Bw%29%5E2=100 ALIGN=MIDDLE  ALT=\"%286%2Bw%29%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Bw=sqrt%28100%29 ALIGN=MIDDLE  ALT=\"6%2Bw=sqrt%28100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Bw=10 ALIGN=MIDDLE  ALT=\"6%2Bw=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=10-6 ALIGN=MIDDLE  ALT=\"w=10-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=4%29 ALIGN=MIDDLE  ALT=\"highlight%28w=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The new height of the wall is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%284feet%29 ALIGN=MIDDLE  ALT=\"highlight%284feet%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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