document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=854203>Question 854203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a triangle with two equal sides 276\". Angle between the two equal sides is 16.3636364.<BR>\n" );
document.write( "What is the length of the other side of the triangle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #514543 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=514543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the other 2 angles of the triangle will be equal to (180 - 16.3636364)/2.\r<BR>\n" );
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document.write( "this makes each of them equal to 81.8181818.\r<BR>\n" );
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document.write( "you can use the law of sines to find the third side.\r<BR>\n" );
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document.write( "the law of sines says that a/sinA = b/sinB = c/sinC\r<BR>\n" );
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document.write( "let A = the angle that is 16.3636364 degrees and let a = x because that's the side opposite that angle that we don't know about.\r<BR>\n" );
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document.write( "let B = one of the angles that is 81.8181818 degrees and let b = 276 because that's the side opposite that angle that we do know about because it was given.\r<BR>\n" );
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document.write( "the part of the law of sines formula that we are interested in is:\r<BR>\n" );
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document.write( "a/sinA = b/sinB\r<BR>\n" );
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document.write( "that becomes x /sin(16.3636364) = 276 / sin(81.8181818)\r<BR>\n" );
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document.write( "multiply both sides of this formula by sin(16.3636364) and you get:\r<BR>\n" );
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document.write( "x = 276 * sin(16.3636364) / sin(818181818) which gets you x = 78.5577909 inches.\r<BR>\n" );
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document.write( "you can confirm this is true by seeing that the ratio based on the law of sines is true.\r<BR>\n" );
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document.write( "78.5577909 / sin(16.3636364) is equal to 278.8381705.\r<BR>\n" );
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document.write( "276 / sin(81.8181818) is equal to 278.8381705.\r<BR>\n" );
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document.write( "the ratios are the same so the solution is good.\r<BR>\n" );
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document.write( "you could also have solved this using the law of cosines as follows:\r<BR>\n" );
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document.write( "the formula to use is c^2 = a^2 + b^2 - 2*a*b*cosC.\r<BR>\n" );
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document.write( "let C be the angle that you know about.<BR>\n" );
document.write( "c is the side opposite this angle.<BR>\n" );
document.write( "a and b are each 276 inches.<BR>\n" );
document.write( "these are the sides that are opposite the other 2 angles that we don't know about and don't need to know about if we are using the law of cosines formula.\r<BR>\n" );
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document.write( "the law of cosines formula becomes:<BR>\n" );
document.write( "c^2 = 276^2 + 276^2 - 2*276*276*cos(16.3636364).<BR>\n" );
document.write( "solve this to get c^2 = 6171.326511<BR>\n" );
document.write( "take the square root of both sides to get:<BR>\n" );
document.write( "x = 78.5577909\r<BR>\n" );
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document.write( "you get the same answer either way.<BR>\n" );
document.write( "that's good.\r<BR>\n" );
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