document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=2912>Question 2912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find if the triangle is acute or obtuse from the sides of given length<BR>\n" );
document.write( "1)5,8,9<BR>\n" );
document.write( "2)24,8,(35<BR>\n" );
document.write( "3)2(10,7,3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1270 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=1270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Your typing was not clear in (2)& (3).\r<BR>\n" );
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document.write( " So far as I know, to determone  if a triangle is acute or obtuse (or<BR>\n" );
document.write( " even to see if it is a valid triangle) we had better use the law of<BR>\n" );
document.write( " cosine.  As, c^2 = a^2 + b^2 - 2 bc cos C. <BR>\n" );
document.write( " So cos C =  (c^2 - a^2 - b^2) / (2bc)<BR>\n" );
document.write( " When c^2 < a^2 + b^2 , angle C is acute.<BR>\n" );
document.write( " When c^2 > a^2 + b^2  , angle C is obtuse.<BR>\n" );
document.write( " Also, the only possible obtuse angle should be the angle opposite to<BR>\n" );
document.write( " the longest side.<BR>\n" );
document.write( " For a valid triangle, we should have a+b > c, b+c >a and c+a > b<BR>\n" );
document.write( " (1) Let (a,b,c)= (5,8,9). <BR>\n" );
document.write( "    At first , check 5+8 > 9 ,OK. It is a legal triangle.<BR>\n" );
document.write( "  (No need to check others as comparing 5+9 and 8, why?)<BR>\n" );
document.write( "    c= 9 is the longest. check angle C<BR>\n" );
document.write( "     Since 5^2 + 8^2 = 25 + 64 = 89 > 9^2  ,so angle C is acute)<BR>\n" );
document.write( "    Hence, this is an acute triangle.\r<BR>\n" );
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document.write( " (2) I suppose, you typed as:<BR>\n" );
document.write( "    (a,b,c)= (24,8,35)<BR>\n" );
document.write( "   Note 24+8 < 35, illegal triangle.<BR>\n" );
document.write( "  If I change it to (a,b,c)= (24,6,35)<BR>\n" );
document.write( "  c= 35 is the longest. check angle C<BR>\n" );
document.write( "     Since 24^2 + 6^2 = 576 + 36 = 612 < 35^2 = 1225  ,so angle C is obtuse)<BR>\n" );
document.write( "    Hence, this is an obtuse triangle.\r<BR>\n" );
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document.write( " Try to read my solutions carefully. And, solve similar questions<BR>\n" );
document.write( " with other given triples. And always remember that the importance<BR>\n" );
document.write( " is the idea not the answer.<BR>\n" );
document.write( " <BR>\n" );
document.write( " Kenny\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
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