document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1030595>Question 1030595</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a question, I was wondering if you could help me with how to find the angles of a triangle that has lengths of 11cm 8cm and 5cm. I am unsure of how to find the angles of the triangles with only having the lengths given how could I do that? I think that I can find it without using a protractor as it is online but I am unsure could you help me find the angles of the triangle please </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645441 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=645441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> look at the diagram.<BR>\n" );
document.write( "see the comments below.\r<BR>\n" );
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document.write( "set your triangle up as follows:\r<BR>\n" );
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document.write( "c = side opposite angle C<BR>\n" );
document.write( "b = side opposite angle B<BR>\n" );
document.write( "a = side opposite angle A\r<BR>\n" );
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document.write( "the law of cosines allows you to find the angles given the sides.\r<BR>\n" );
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document.write( "that law states:\r<BR>\n" );
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document.write( "c^2 = a^2 + b^2 - 2ab*cos(C)\r<BR>\n" );
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document.write( "a^2 = b^2 + c^2 - 2bc*cos(A)\r<BR>\n" );
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document.write( "b^2 = a^2 + c^2 - 2ac*cos(B)\r<BR>\n" );
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document.write( "you would need to solve for two of the angles and then you can get the third angle automatically by subtracting the sum of those two angles from 180.\r<BR>\n" );
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document.write( "i'll solve for angle C and for angle A.\r<BR>\n" );
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document.write( "for angle C, start with:\r<BR>\n" );
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document.write( "c^2 = a^2 + b^2 - 2ab*cos(C)\r<BR>\n" );
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document.write( "solve for cos(C) to get:\r<BR>\n" );
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document.write( "cos(C) = (a^2 + b^2 - c^2) / (2*a*b)\r<BR>\n" );
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document.write( "replace letters with values to get:\r<BR>\n" );
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document.write( "cos(C) = (8^2 + 11^2 - 5^2) / (2*8*5)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "cos(C) = .9090909091\r<BR>\n" );
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document.write( "solve for C to get:\r<BR>\n" );
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document.write( "C = arccos(.9090909091) = 24.61997733 degrees.\r<BR>\n" );
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document.write( "for angle A, start with:\r<BR>\n" );
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document.write( "a^2 = b^2 + c^2 - 2bc*cos(A)\r<BR>\n" );
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document.write( "solve for cos(A) to get:\r<BR>\n" );
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document.write( "cos(A) = (b^2 + c^2 - a^2) / (2*b*c)\r<BR>\n" );
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document.write( "replace letters with values to get:\r<BR>\n" );
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document.write( "cos(A) = (11^2 + 5^2 - 8^2) / (2*11*5)\r<BR>\n" );
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document.write( "solve for cos(A) to get:\r<BR>\n" );
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document.write( "cos(A) = .7454545455\r<BR>\n" );
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document.write( "solve for A to get:\r<BR>\n" );
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document.write( "A = arccos(.7454545455) = 41.80184419 degrees.\r<BR>\n" );
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document.write( "now that you have angle A and angle C, you can solve for angle B by subtracting their sum from 180.\r<BR>\n" );
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document.write( "angle B = 180 - 24.61997733 - 41.80184419 = 113.5781785 degrees.\r<BR>\n" );
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document.write( "you could also solve for angle B using the law of cosines again.\r<BR>\n" );
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document.write( "you would get the same answer.\r<BR>\n" );
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document.write( "here's a lesson on law of sines and law of cosines that can help you understand what the formulas are and how to use them.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.regentsprep.org/regents/math/algtrig/ATT12/indexATT12.htm\" target = \"_blank\">http://www.regentsprep.org/regents/math/algtrig/ATT12/indexATT12.htm</a>\r<BR>\n" );
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document.write( "select law of sines lesson and then select law of cosines lesson.\r<BR>\n" );
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document.write( "here's another reference talking about the same thing.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.mathwarehouse.com/trigonometry/law-of-sines-and-cosines.php\" target = \"_blank\">http://www.mathwarehouse.com/trigonometry/law-of-sines-and-cosines.php</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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