document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203040>Question 1203040</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this<BR>\n" );
document.write( "The sides of a triangle have lengths 11, 15, and k where k is an integer. For how many values of k, is <BR>\n" );
document.write( "the triangle obtuse? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838283 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838283\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "In a right triangle with the standard notation with c being the length of the longest side (hypotenuse), the relationship <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > holds.<br><BR>\n" );
document.write( "For a triangle to be obtuse, again using c to denote the length of the longest side, the relationship <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2%3Ea%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2%3Ea%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > must hold.<br><BR>\n" );
document.write( "In this problem, there are two cases to consider -- the longest side can be either k or 15.<br><BR>\n" );
document.write( "(1) k is the longest side<br><BR>\n" );
document.write( "The triangle inequality tells us that k<11+15=26.<br><BR>\n" );
document.write( "For the triangle to be obtuse, we need to have<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2%3E11%5E2%2B15%5E2 ALIGN=MIDDLE  ALT=\"k%5E2%3E11%5E2%2B15%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2%3E346 ALIGN=MIDDLE  ALT=\"k%5E2%3E346\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3E18.6 ALIGN=MIDDLE  ALT=\"k%3E18.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximately<br><BR>\n" );
document.write( "The integers greater than 18.6 and less than 26 are 19 through 25 inclusive -- that's 7 possible integer values for k.<br><BR>\n" );
document.write( "(2) 15 is the longest side<br><BR>\n" );
document.write( "Now the triangle inequality tells us k>15-11=4.<br><BR>\n" );
document.write( "For the triangle to be obtuse, we need to have<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%5E2%3Ek%5E2%2B11%5E2 ALIGN=MIDDLE  ALT=\"15%5E2%3Ek%5E2%2B11%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225-121%3Ek%5E2 ALIGN=MIDDLE  ALT=\"225-121%3Ek%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2%3C104 ALIGN=MIDDLE  ALT=\"k%5E2%3C104\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3C10.2 ALIGN=MIDDLE  ALT=\"k%3C10.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximately<br><BR>\n" );
document.write( "The integers greater than 4 and less than 10.2 are 5 through 10 inclusive -- that's 6 possible integer values for k.<br><BR>\n" );
document.write( "ANSWER: 7+6 = 13<br><BR>\n" );
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