document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=843492>Question 843492</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the angle of elevation of the top of a tree from a point P is 7 degree. After walking 30m towards the tree, the angle of elevation becomes 9.1. Find the height of the 10? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #508606 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=508606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is a sketch illustrating the problem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-5.5%2C0.5%2C-0.7%2C3.3%2C%0D%0Aline%28-5.5%2C0%2C0.5%2C0%29%2Cline%280%2C0%2C0%2C3%29%2C%0D%0Ablue%28line%28-5%2C0%2C0%2C3%29%29%2Cblue%28line%28-3%2C0%2C0%2C3%29%29%2C%0D%0Arectangle%28-0.2%2C0.2%2C0%2C0%29%2Clocate%28-5.02%2C0.3%2CP%29%2C%0D%0Ablue%28arc%28-5%2C0%2C2%2C2%2C-31%2C0%29%29%2Clocate%28-4.4%2C0.5%2C7%5Eo%29%2C%0D%0Ablue%28arc%28-3%2C0%2C2%2C2%2C-45%2C0%29%29%2Clocate%28-2.7%2C0.5%2C9.1%5Eo%29%2C%0D%0Alocate%28-4.22%2C-0.25%2C30m%29%2Clocate%28-1.55%2C-0.25%2Cd%29%2C%0D%0Aarrow%28-3%2C-0.2%2C-5%2C-0.2%29%2Carrow%28-5%2C-0.2%2C-3%2C-0.2%29%2C%0D%0Aarrow%28-1%2C-0.2%2C-3%2C-0.2%29%2Carrow%28-2%2C-0.2%2C0%2C-0.2%29%2C%0D%0Alocate%28-0.18%2C1.6%2Ch%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > To show those right triangles clearly, I had to draw the angles much wider than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5Eo ALIGN=MIDDLE  ALT=\"7%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.1%5Eo ALIGN=MIDDLE  ALT=\"9.1%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The height of the tree 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( "After walking <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30m ALIGN=MIDDLE  ALT=\"30m\"   DISABLED_style= \"max-width:90%; height:auto;\" > towards the tree, at a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the base of the tree, the angle of elevation becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.1%5Eo ALIGN=MIDDLE  ALT=\"9.1%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%289.1%5Eo%29=h%2Fd ALIGN=MIDDLE  ALT=\"tan%289.1%5Eo%29=h%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fh=1%2Ftan%289.1%5Eo%29 ALIGN=MIDDLE  ALT=\"d%2Fh=1%2Ftan%289.1%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From point P, at a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2B30m ALIGN=MIDDLE  ALT=\"d%2B30m\"   DISABLED_style= \"max-width:90%; height:auto;\" >  from the base of the tree, the angle of elevation was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.1%5Eo ALIGN=MIDDLE  ALT=\"9.1%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%287%5Eo%29=h%2F%28d%2B30m%29 ALIGN=MIDDLE  ALT=\"tan%287%5Eo%29=h%2F%28d%2B30m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2B30m%29%2Fh=1%2Ftan%287%5Eo%29 ALIGN=MIDDLE  ALT=\"%28d%2B30m%29%2Fh=1%2Ftan%287%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2B30m%29%2Fh-d%2Fh=1%2Ftan%287%5Eo%29-1%2Ftan%289.1%5Eo%29 ALIGN=MIDDLE  ALT=\"%28d%2B30m%29%2Fh-d%2Fh=1%2Ftan%287%5Eo%29-1%2Ftan%289.1%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2B30m-d%29%2Fh=1%2Ftan%287%5Eo%29-1%2Ftan%289.1%5Eo%29 ALIGN=MIDDLE  ALT=\"%28d%2B30m-d%29%2Fh=1%2Ftan%287%5Eo%29-1%2Ftan%289.1%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30m%2Fh=1%2Ftan%287%5Eo%29-1%2Ftan%289.1%5Eo%29 ALIGN=MIDDLE  ALT=\"30m%2Fh=1%2Ftan%287%5Eo%29-1%2Ftan%289.1%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From now on we calculate approximate values, rounding as needed.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30m%2Fh=1%2F0.122785-1%2F0.160174 ALIGN=MIDDLE  ALT=\"30m%2Fh=1%2F0.122785-1%2F0.160174\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30m%2Fh=8.1443-1%2F6.2432 ALIGN=MIDDLE  ALT=\"30m%2Fh=8.1443-1%2F6.2432\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30m%2Fh=1.9011 ALIGN=MIDDLE  ALT=\"30m%2Fh=1.9011\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30m%2F1.9011=h ALIGN=MIDDLE  ALT=\"30m%2F1.9011=h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=highlight%2815.78m%29 ALIGN=MIDDLE  ALT=\"h=highlight%2815.78m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );