document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=668529>Question 668529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> at a point on the ground 24ft from the base of a tree, the distance to the top of the tree if 4ft more than 3 times the height of the tree. 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 #415638 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=415638\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let h = height of tree\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If \"at a point on the ground 24ft from the base of a tree, the distance to the top of the tree if 4ft more than 3 times the height of the tree\", then the distance is 3h+4 (and this is the hypotenuse while the other two values are the legs of a right triangle)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now use the Pythagorean theorem\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a^2 + b^2 = c^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "24^2 + h^2 = (3h+4)^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "576 + h^2 = 9h^2 + 24h + 16\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0 = 9h^2 + 24h + 16 - h^2 - 576\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0 = 8h^2 + 24h - 560\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "8h^2 + 24h - 560 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "8(h^2 + 3h - 70) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "8(h+10)(h-7) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h+10 = 0 or h-7 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h = -10 or h = 7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Toss out the negative height (since it doesn't make sense) to get the only answer of h = 7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the height of the tree is 7 ft. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );