document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=719674>Question 719674</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Bubba and Madge are lying on the grass 100 yards apart.  Ideally, they would be making googly eyes at one another, but unfortunately a pine tree stands alone somewhere between them.   Madge notices that there is a 17 degree angle of elevation to the top of the tree – Bubba discovers there is a 12 degree angle of elevation to the tree’s top.  To the nearest inch, how tall is the tree?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #441455 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=441455\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For simplicity of calculation, let Bubba's angle = B and Madge's angle = M<BR>\n" );
document.write( "Let x = the distance along the ground from Madge to the tree<BR>\n" );
document.write( "Then 100 - x = the distance along the ground from Bubba to the tree<BR>\n" );
document.write( "Let h = the height of the tree<BR>\n" );
document.write( "tan(M) = h/x -> x = h/tan(M)<BR>\n" );
document.write( "tan(B) = h/(100-x) -> tan(B) = h/(100-(h/tan(M))<BR>\n" );
document.write( "Simplify and solve for h:<BR>\n" );
document.write( "tan(B)(100 - h/tan(M)) = h<BR>\n" );
document.write( "h = 100tan(B)/(1+tan(B)/tan(M))<BR>\n" );
document.write( "Divide top and bottom by tan(B):<BR>\n" );
document.write( "h = 100/(1/tan(B) + 1/tan(M))<BR>\n" );
document.write( "Putting in the numbers gives h = 12.5384 yds<BR>\n" );
document.write( "0.5384 yds = 19.38 inch<BR>\n" );
document.write( "So to the nearest inch the tree is 12 yds 19 inch </SPAN>\n" );
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