document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388566>Question 388566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the missing side length that will form an obtuse triangle with sides of length 8 and 10. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #274928 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=274928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose the missing side length is x. A triangle is obtuse if\r<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+%3C+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+%3C+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for some side lengths a, b, c (this is a result from the law of cosines). Therefore,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+8%5E2+%3C+10%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+8%5E2+%3C+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+6 ALIGN=MIDDLE  ALT=\"x+%3C+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but x must be greater than 2 due to the triangle inequality.\r<BR>\n" );
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document.write( "Or, if x is the longest side, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E2+%2B+10%5E2+%3C+x%5E2 ALIGN=MIDDLE  ALT=\"8%5E2+%2B+10%5E2+%3C+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+sqrt%28164%29 ALIGN=MIDDLE  ALT=\"x+%3E+sqrt%28164%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. x is less than 18 also because of the triangle inequality. Therefore, any real number in the sets (2, 6), (sqrt(164), 18) will make the triangle obtuse. </SPAN>\n" );
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