document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209390>Question 1209390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sides of a triangle measure 4, 9, and 11. Is this a right triangle? If not then is it acute or obtuse? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848739 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=848739\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "We use the Converse of the Pythagorean Theorem. <BR>\n" );
document.write( "Here are the three possibilities:<ul><li>If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then it's a right triangle.</li><li>If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2+%3E+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2+%3E+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then the triangle is acute.</li><li>If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2+%3C+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2+%3C+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then the triangle is obtuse.</li></ul>a,b,c are the sides of the triangle.<BR>\n" );
document.write( "c is always the longest side. The a,b can be in any order.\r<BR>\n" );
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document.write( "a = 4, b = 9, c = 11 are the three sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2+=+4%5E2%2B9%5E2+=+16%2B81+=+97 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2+=+4%5E2%2B9%5E2+=+16%2B81+=+97\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+11%5E2+=+121 ALIGN=MIDDLE  ALT=\"c%5E2+=+11%5E2+=+121\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In short,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2+=+97 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2+=+97\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+121 ALIGN=MIDDLE  ALT=\"c%5E2+=+121\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The results 97 and 121 aren't equal, so the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > case is false.<BR>\n" );
document.write( "This is <font color=red><u>not</u> a right triangle</font>. <BR>\n" );
document.write( "The result of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is smaller than the result of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2 ALIGN=MIDDLE  ALT=\"c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since 97 < 121) so we conclude that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2+%3C+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2+%3C+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is case.<BR>\n" );
document.write( "The triangle is <font color=red>obtuse</font>. \r<BR>\n" );
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document.write( "You can confirm this using an online tool such as <a  rel=nofollow HREF=\"https://www.calculator.net/triangle-calculator.html\">this one</a> or you can use <a  rel=nofollow HREF=\"https://www.geogebra.org/calculator/zp9hpqpe\">GeoGebra</a> (the GeoGebra link may take a bit of time to load).<BR>\n" );
document.write( "There are many other similar online tools. \r<BR>\n" );
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document.write( "Answer: <font color=red>Obtuse</font><BR>\n" );
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