document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=927333>Question 927333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On a hill, inclined at an angle of 14.2o with the horizontal stands a vertical tower. At a point P, 62.5 meters down the hill from the foot of the tower, the angle of elevation of the top of the tower is 43.6o . How tall is the tower? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #562922 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=562922\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is a sketch with the necessary imaginary horizontal and vertical lines drawn in green:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-70%2C10%2C-10%2C70%2C%0D%0Agreen%28triangle%28-200%2C0%2C0%2C0%2C0%2C200%29%29%2C%0D%0Agreen%28triangle%28-300%2C0%2C100%2C0%2C100%2C300%29%29%2C%0D%0Agreen%28rectangle%28-2%2C0%2C0%2C2%29%29%2C%0D%0Aline%28-60.59%2C0%2C10%2C17.86%29%2Cline%280%2C15.33%2C0%2C58%29%2C%0D%0Ared%28line%28-60.59%2C0%2C0%2C58%29%29%2C%0D%0Aarc%28-60.59%2C0%2C15%2C15%2C-43.6%2C0%29%2Clocate%28-54.5%2C8%2C43.6%5Eo%29%2C%0D%0Aarc%28-60.59%2C0%2C30%2C30%2C-14.2%2C0%29%2Clocate%28-45.59%2C5%2C14.2%5Eo%29%2C%0D%0Alocate%28-61%2C0%2CP%29%2Clocate%280%2C0%2CU%29%2C%0D%0Alocate%280.5%2C15.3%2CB%29%2Clocate%280.5%2C60%2CT%29%2C%0D%0Alocate%280.5%2C37%2Ch%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > We need to calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the height of tower <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BT ALIGN=MIDDLE  ALT=\"BT\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We can use law of sines applied to triangle BPT:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Fsin%28BPT%29=62.5m%2Fsin%28PTB%29 ALIGN=MIDDLE  ALT=\"h%2Fsin%28BPT%29=62.5m%2Fsin%28PTB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We just need to calculate the measure of those angles<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BPT=43.6%5Eo-14.2%5Eo=29.4%5Eo ALIGN=MIDDLE  ALT=\"BPT=43.6%5Eo-14.2%5Eo=29.4%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and PTB is part of right triangle PTU, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PTB=90%5Eo-43.6%5Eo=46.4%5Eo ALIGN=MIDDLE  ALT=\"PTB=90%5Eo-43.6%5Eo=46.4%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Fsin%2829.4%5Eo%29=62.5m%2Fsin%2846.4%5Eo%29 ALIGN=MIDDLE  ALT=\"h%2Fsin%2829.4%5Eo%29=62.5m%2Fsin%2846.4%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using approximate values,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2F0.490904=62.5m%2F0.724172 ALIGN=MIDDLE  ALT=\"h%2F0.490904=62.5m%2F0.724172\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0.490904%2A62.5m%2F0.724172 ALIGN=MIDDLE  ALT=\"h=0.490904%2A62.5m%2F0.724172\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28h=42.4m%29 ALIGN=MIDDLE  ALT=\"highlight%28h=42.4m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to one decimal place). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );