document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189460>Question 189460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times 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 #142133 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=142133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">     At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times height of the tree. Find the height of the tree. <BR>\n" );
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document.write( "Drawing a diagram of the problem will help you \"see\" the solution.<BR>\n" );
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document.write( "You will be applying the Pythagorean theorem.<BR>\n" );
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document.write( "Let h = height of the tree<BR>\n" );
document.write( "then<BR>\n" );
document.write( "3h+1 is the hypotenuse<BR>\n" );
document.write( "the other two sides are:<BR>\n" );
document.write( "h and 35<BR>\n" );
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document.write( "h^2 + 35^2 = (3h+1)^2<BR>\n" );
document.write( "h^2 + 35^2 = (3h+1)(3h+1)<BR>\n" );
document.write( "h^2 + 35^2 = 9h^2 + 6h + 1<BR>\n" );
document.write( "35^2 = 8h^2 + 6h + 1<BR>\n" );
document.write( "1225 = 8h^2 + 6h + 1<BR>\n" );
document.write( "0 = 8h^2 + 6h - 1224<BR>\n" );
document.write( "0 = 4h^2 + 3h - 612<BR>\n" );
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document.write( "Applying the quadratic formula gives us:<BR>\n" );
document.write( "h = {12, -12.75}<BR>\n" );
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document.write( "Toss out the negative solution leaves us with:<BR>\n" );
document.write( "h = 12 feet (height of tree)<BR>\n" );
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document.write( "Details of quadratic follows:<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ah%5E2%2Bbh%2Bc=0 ALIGN=MIDDLE  ALT=\"ah%5E2%2Bbh%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4h%5E2%2B3h%2B-612+=+0 ALIGN=MIDDLE  ALT=\"4h%5E2%2B3h%2B-612+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"h%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%283%29%5E2-4%2A4%2A-612=9801 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283%29%5E2-4%2A4%2A-612=9801\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=9801 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-3%2B-sqrt%28+9801+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-3%2B-sqrt%28+9801+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B1%5D+=+%28-%283%29%2Bsqrt%28+9801+%29%29%2F2%5C4+=+12 ALIGN=MIDDLE  ALT=\"h%5B1%5D+=+%28-%283%29%2Bsqrt%28+9801+%29%29%2F2%5C4+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B2%5D+=+%28-%283%29-sqrt%28+9801+%29%29%2F2%5C4+=+-12.75 ALIGN=MIDDLE  ALT=\"h%5B2%5D+=+%28-%283%29-sqrt%28+9801+%29%29%2F2%5C4+=+-12.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4h%5E2%2B3h%2B-612 ALIGN=MIDDLE  ALT=\"4h%5E2%2B3h%2B-612\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4h%5E2%2B3h%2B-612+=+4%28h-12%29%2A%28h--12.75%29 ALIGN=MIDDLE  ALT=\"4h%5E2%2B3h%2B-612+=+4%28h-12%29%2A%28h--12.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 12, -12.75.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B3%2Ax%2B-612+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B3%2Ax%2B-612+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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