document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=827668>Question 827668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A tree on top of a hill casts a shadow of 20 m long down the hill.  Of the angle of elevation of the sun is 75 degrees and the hill is inclined 45 degrees, find the height of the tree </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #498967 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=498967\">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%28200%2C440%2C-5%2C25%2C-5%2C61%2C%0D%0Aline%28-5%2C-5%2C25%2C25%29%2C%0D%0Aline%280%2C0%2C30%2C0%29%2C%0D%0Alocate%2814.5%2C0%2Chorizontal%29%2Clocate%2818%2C-1.8%2Cline%29%2C%0D%0Alocate%2818%2C18%2Chill%29%2Clocate%2818%2C16.2%2Cslope%29%2C%0D%0Atriangle%280%2C0%2C14.14%2C0%2C14.14%2C52.78%29%2C%0D%0Arectangle%2814.14%2C0%2C13.14%2C1%29%2C%0D%0Alocate%2814.64%2C2.3%2CP%29%2Clocate%2814.64%2C14.14%2CR%29%2C%0D%0Alocate%2814.64%2C52.78%2CT%29%2Clocate%280%2C0%2CS%29%2C%0D%0Ared%28arrow%2814.14%2C52.78%2C16.08%2C60%29%29%2C%0D%0Alocate%2816.5%2C60.5%2Cto%29%2Clocate%2819.5%2C60.5%2Csun%29%2C%0D%0Agreen%28line%2814.14%2C14.14%2C14.14%2C52.78%29%29%2Clocate%2814.5%2C35%2Cgreen%28tree%29%29%2C%0D%0Alocate%281.8%2C3.5%2C45%5Eo%29%2Carc%280%2C0%2C12%2C12%2C-45%2C0%29%2C%0D%0Alocate%284%2C12%2C75%5Eo%29%2Carc%280%2C0%2C20%2C20%2C-75%2C0%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > RS = 20 m = shadow of tree<BR>\n" );
document.write( "Consider right triangle RSP.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PS=RS%2Acos%2845%5Eo%29=%2820m%29%28sqrt%282%29%2F2%29=14.14m ALIGN=MIDDLE  ALT=\"PS=RS%2Acos%2845%5Eo%29=%2820m%29%28sqrt%282%29%2F2%29=14.14m\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to nearest 0.1m)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RP=RS%2Asin%2845%5Eo%29=%2820m%29%28sqrt%282%29%2F2%29=14.14m ALIGN=MIDDLE  ALT=\"RP=RS%2Asin%2845%5Eo%29=%2820m%29%28sqrt%282%29%2F2%29=14.14m\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to nearest 0.1m)<BR>\n" );
document.write( "Consider right triangle TSP.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PT=PS%2Atan%2875%5Eo%29=%2814.14m%29%2A3.732=52.78m ALIGN=MIDDLE  ALT=\"PT=PS%2Atan%2875%5Eo%29=%2814.14m%29%2A3.732=52.78m\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to nearest 0.1m)<BR>\n" );
document.write( "The height of the tree is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RT=PT-RP=52.78m-14.14m=38.64m ALIGN=MIDDLE  ALT=\"RT=PT-RP=52.78m-14.14m=38.64m\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to nearest 0.1m).<BR>\n" );
document.write( "(Maybe it should be rounded to 39 meters, since the shadow's length and angles do not seem to have been measured with such fine precision).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );