document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76911>Question 76911</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two children are trying to cross a stream. They want to use a log that goes from one bank to the other. If the left bank is 9 feet higher than the right bank and the stream is 12 feet wide, how long must a log be to just barely reach? \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 #55134 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=55134\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a \"right triangle\" problem.<BR>\n" );
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document.write( "If you measure horizontally from the level of the right bank, the distance across the stream<BR>\n" );
document.write( "is 12 feet.  But at the point that the horizontal distance reaches the left bank you then<BR>\n" );
document.write( "need to go vertically upward 9 feet to get to the edge of the left bank.  These two <BR>\n" );
document.write( "distances are the legs of a right triangle and are 90 degrees to each other.  The length<BR>\n" );
document.write( "of the log that goes from the edge of the right bank upward at a slant to the edge of the<BR>\n" );
document.write( "left bank is the hypotenuse or long side of the of this triangle.<BR>\n" );
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document.write( "To find the length of the hypotenuse we can use the Pythagorean theorem which says that if<BR>\n" );
document.write( "you square the length of each leg of a right triangle and add these two squares, the result<BR>\n" );
document.write( "will be the square of the length of the hypotenuse. In equation form this can be written as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Where \"a\" and \"b\" are the lengths of the legs and \"c\" is the length of the hypotenuse.<BR>\n" );
document.write( "In this problem we can say that \"a\" is 9 ft, \"b\" is 12 ft, and c is the unknown length of<BR>\n" );
document.write( "the log.  Substitute these values into the equation and it becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E2+%2B+12%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"9%5E2+%2B+12%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Squaring each of the numbers on the left side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81+%2B+144+=+c%5E2 ALIGN=MIDDLE  ALT=\"81+%2B+144+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add the terms on the left side and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225+=+c%5E2 ALIGN=MIDDLE  ALT=\"225+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And now you can solve for \"c\" by taking the square root of both sides.  When you do that<BR>\n" );
document.write( "the equation is reduced to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28225%29+=+15+=+c ALIGN=MIDDLE  ALT=\"sqrt%28225%29+=+15+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the log must be 15 ft long to barely reach from the edge of the right bank to the edge<BR>\n" );
document.write( "of the left bank.<BR>\n" );
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document.write( "Hope this is an understandable explanation and that you can picture what I have tried to<BR>\n" );
document.write( "explain in words. Sometimes it helps to visualize a problem if you make a sketch of the<BR>\n" );
document.write( "situation ... in this case showing the width of the stream (12 ft), the difference<BR>\n" );
document.write( "in the height of the two banks (9 ft), and the slant distance of the log that goes from<BR>\n" );
document.write( "the edge of the lower right bank to the edge of the higher left bank. </SPAN>\n" );
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