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 #415641 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=415641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we were to draw a picture of a right triangle where the base is the distance from the point to the base of the tree, the height is the height of the tree and the distance from the point to the top of the tree is the hypotenuse, we can apply the Pythagorean THM:\r<BR>\n" );
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document.write( "Let a be the height of the tree.\r<BR>\n" );
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document.write( "Let b be the point to the base.\r<BR>\n" );
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document.write( "Let c be the point to the top.\r<BR>\n" );
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document.write( "a^2 + b^2 = c^2\r<BR>\n" );
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document.write( "a^2 + 24^2 = (3a+4)^2\r<BR>\n" );
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document.write( "a^2 + 576 = 9a^2 + 24a + 16\r<BR>\n" );
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document.write( "-8a^2 -24a + 560 = 0\r<BR>\n" );
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document.write( "-8(a^2+3a-70)\r<BR>\n" );
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document.write( "(a+10)(a-7) \r<BR>\n" );
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document.write( "So a = 7 or a = -10.\r<BR>\n" );
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document.write( "Height can't be negative, so we only accept the positive answer leaving us with a = 7 ft. </SPAN>\n" );
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