document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=919082>Question 919082</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the lengths of the sides of a triangle are 11cm, 15cm, and k cm, where k is an integer. For how many values of k is the triangle acute? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #557460 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39625)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=557460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For HOW MANY VALUES of k?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%5E2%2B15%5E2%3Ek%5E2 ALIGN=MIDDLE  ALT=\"11%5E2%2B15%5E2%3Ek%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "Also need to apply this to the two other sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%5E2%2Bk%5E2%3E15%5E2 ALIGN=MIDDLE  ALT=\"11%5E2%2Bk%5E2%3E15%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%5E2%2Bk%5E2%3E11%5E2 ALIGN=MIDDLE  ALT=\"15%5E2%2Bk%5E2%3E11%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Not so much of how many values of k; but more important, which values of k.<BR>\n" );
document.write( "Important rule here is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3E0 ALIGN=MIDDLE  ALT=\"k%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "(1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3C18.601 ALIGN=MIDDLE  ALT=\"k%3C18.601\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3E10.20 ALIGN=MIDDLE  ALT=\"k%3E10.20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(3)<BR>\n" );
document.write( "... k must not be negative.\r<BR>\n" );
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document.write( "k can be any value such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2810.2%3Ck%3C18.601%29 ALIGN=MIDDLE  ALT=\"highlight%2810.2%3Ck%3C18.601%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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