document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105445>Question 1105445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> an adult and a young boy, standing on the ground are one metre apart .the height of the adult is 2 times the height of young boy. if at the mid-point of the line joining their feet the angular elevation of their tops are complementary , find the height of the young boy </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #720281 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=720281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A very, very small adult!<BR>\n" );
document.write( " <BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the height of the boy, in metres.<BR>\n" );
document.write( "If the man and boy are standing on level ground,<BR>\n" );
document.write( "their heights can be represented as vertical lines,<BR>\n" );
document.write( "perpendicular to the horizontal ground.<BR>\n" );
document.write( "The sketch below shows the two humans' heights,<BR>\n" );
document.write( "the ground under them,<BR>\n" );
document.write( "and the line segments connecting point M<BR>\n" );
document.write( "(the mid-point of the line joining their feet)<BR>\n" );
document.write( "to the top of their heights.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C300%2C-7.5%2C7.5%2C-1%2C8%2C%0D%0Aline%28-8%2C0%2C8%2C0%29%2Ctriangle%28-5%2C0%2C0%2C0%2C-5%2C3.536%29%2C%0D%0Arectangle%28-5%2C0%2C-4.8%2C0.2%29%2Crectangle%285%2C0%2C4.8%2C0.2%29%2C%0D%0Atriangle%280%2C0%2C5%2C0%2C5%2C7.071%29%2Clocate%28-3%2C0.5%2C0.5m%29%2C%0D%0Ared%28line%285%2C0%2C5%2C7.071%29%29%2Cgreen%28line%28-5%2C0%2C-5%2C3.536%29%29%2C%0D%0Alocate%282%2C0.5%2C0.5m%29%2Clocate%285.1%2C6%2Cred%28man%29%29%2C%0D%0Alocate%28-5.8%2C2.8%2Cgreen%28boy%29%29%2Clocate%285.5%2C0%2Clevel%29%2C%0D%0Alocate%285.5%2C-0.3%2Cground%29%2Clocate%28-4.9%2C2%2Cx%29%2Clocate%284.4%2C4%2C2x%29%2C%0D%0Alocate%28-0.1%2C0%2CM%29%2Cred%28arc%280%2C0%2C2%2C2%2C-54.7%2C0%29%29%2C%0D%0Agreen%28arc%280%2C0%2C2%2C2%2C180%2C215.3%29%29%2Cgreen%28arc%280%2C0%2C2.05%2C2.05%2C180%2C215.3%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The red and green arcs show the angles of elevation from M to the top of the adult's and boy's heads.<BR>\n" );
document.write( "Those two angles are complementary,<BR>\n" );
document.write( "meaning that their measures add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%5Eo ALIGN=MIDDLE  ALT=\"90%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "As the two triangles are right triangles,<BR>\n" );
document.write( "the acute angles in each triangle are also complementary,<BR>\n" );
document.write( "meaning that their measures add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%5Eo ALIGN=MIDDLE  ALT=\"90%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "As a consequence, for each triangle, the angle not marked with an arc<BR>\n" );
document.write( "is complementary to the marked angle in the other triangle.<BR>\n" );
document.write( "That makes the triangles similar.<BR>\n" );
document.write( "Similar triangles have proportional side lengths.<BR>\n" );
document.write( "With side length measured in m,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F0.5=0.5%2Fx ALIGN=MIDDLE  ALT=\"2x%2F0.5=0.5%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2=0.5%2A0.5 ALIGN=MIDDLE  ALT=\"2x%5E2=0.5%2A0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=0.25%2F2 ALIGN=MIDDLE  ALT=\"x%5E2=0.25%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=0.125 ALIGN=MIDDLE  ALT=\"x%5E2=0.125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%280.125%29=approximately ALIGN=MIDDLE  ALT=\"x=sqrt%280.125%29=approximately\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.3536 ALIGN=MIDDLE  ALT=\"0.3536\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That would make the height of the boy <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.354m%29 ALIGN=MIDDLE  ALT=\"highlight%280.354m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the height of the adult would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%280.3536m%29=0.707m ALIGN=MIDDLE  ALT=\"2%280.3536m%29=0.707m\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That would make that adult a very strong contender for the title of shortest man (or woman) alive. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );