document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1059132>Question 1059132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the number of possible triangles that can be draw based on the given information:\r<BR>\n" );
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document.write( "In triangle DEF, angle D = 66 degrees; d = 15 cm; and f = 11 cm \r<BR>\n" );
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document.write( "I would really appreciate some help with this question.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #674321 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=674321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe this has to do with the law of sines.\r<BR>\n" );
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document.write( "that law says that a / sin(A) = b / sin(B) = c / sin(C).\r<BR>\n" );
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document.write( "this can also be written as d / sin(D) = e / sin(E) = f / sin(F)\r<BR>\n" );
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document.write( "your triangle is DEF.\r<BR>\n" );
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document.write( "side opposite angle D is d.<BR>\n" );
document.write( "side opposite angle E is e.<BR>\n" );
document.write( "side opposite angle F is f.\r<BR>\n" );
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document.write( "you are given that angle D is equal to 66 degrees and side d is equal to 15 and side f is equal to 11.\r<BR>\n" );
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document.write( "by the law of sines, you get d / sin(D) = f / sin(F).\r<BR>\n" );
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document.write( "this becomes 15 / sin(66) = 11 / sin(F)\r<BR>\n" );
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document.write( "solve for sin(F) to get sin(F) = 11 * sin(66) / 15\r<BR>\n" );
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document.write( "solve for sin(F) to get sin(F) = .6699333356\r<BR>\n" );
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document.write( "solve for F to get F = arcsin(.6699333356) = 42.06191982 degrees.\r<BR>\n" );
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document.write( "since the sum of angle D and F is less than 180, then at least 1 triangle is possible.\r<BR>\n" );
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document.write( "to see if a second trianlge is possible, take 180 - 42.06191982 degrees to get 137.9380802 degrees.\r<BR>\n" );
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document.write( "add that to 66 degrees and the sum is greater than 180, so only 1 triangle is possible.\r<BR>\n" );
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document.write( "here's a reference that might help you to understand.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.regentsprep.org/regents/math/algtrig/att12/lawofsinesAmbiguous.htm\" target = \"_blank\">http://www.regentsprep.org/regents/math/algtrig/att12/lawofsinesAmbiguous.htm</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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