document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129201>Question 1129201</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The angle of elevation from a point on the ground to the top of a tree is 35.3 degrees. The angle of elevation from a point 20 ft farther back to the top of the tree is 23.3 degrees. Find the height of the tree to 2 decimal places.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #745795 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=745795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The angle of elevation from a point on the ground to the top of a tree is 35.3 degrees.<BR>\n" );
document.write( " The angle of elevation from a point 20 ft farther back to the top of the tree is 23.3 degrees.<BR>\n" );
document.write( " Find the height of the tree to 2 decimal places.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The tree top, bottom and points on the ground form right triangles<BR>\n" );
document.write( "let t = the height of the tree<BR>\n" );
document.write( "let d = distance from the point on the ground when the angle is 35.3 degrees<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(d+20) = distance from the further point on the ground when the angle is 23.3 degrees<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use the tangent of the angles h = side opposite<BR>\n" );
document.write( "Two position equations<BR>\n" );
document.write( "tan(23.3) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2F%28d%2B20%29 ALIGN=MIDDLE  ALT=\"h%2F%28d%2B20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = tan(23.3)*(d+20)<BR>\n" );
document.write( "h = .43067d + 8.613<BR>\n" );
document.write( "and<BR>\n" );
document.write( "tan(35.3) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Fd ALIGN=MIDDLE  ALT=\"h%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = tan(35.3) * d<BR>\n" );
document.write( "h = .708d<BR>\n" );
document.write( "h = h solve for d<BR>\n" );
document.write( ".708d = .43067d + 8.613<BR>\n" );
document.write( ".708d -.43067d = 8.613<BR>\n" );
document.write( ".277d = 8.613<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.613%2F.277 ALIGN=MIDDLE  ALT=\"8.613%2F.277\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = 31.10 ft<BR>\n" );
document.write( "Find h<BR>\n" );
document.write( "h = .708(31.1)<BR>\n" );
document.write( "h = 22.02 ft is the height of the tree<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this using the other position which is 51.1 ft from the tree<BR>\n" );
document.write( "tan(23.3) * 51.1 = 22.01 ft, close enough?<BR>\n" );
document.write( ".\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );