document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1036433>Question 1036433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diagonals of a parallelogram have lengths of 12cm and 18cm and the angle between them is 72degree.<BR>\n" );
document.write( "Find the lengths of the sides of the parallelogram.\r<BR>\n" );
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document.write( "I have 1 side which is 9.1 by using the cosine rule but the second side , i do not know how to do. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #651091 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=651091\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "The diagonals of a parallelogram have lengths of 12cm and 18cm and the angle between them is 72degree.<BR>\n" );
document.write( "Find the lengths of the sides of the parallelogram.\r<BR>\n" );
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document.write( "I have 1 side which is 9.1 by using the cosine rule but the second side , i do not know how to do.<BR>\n" );
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document.write( "Make a sketch of the parallelogram.<BR>\n" );
document.write( "Draw the diagonals.<BR>\n" );
document.write( "Mark the intersection point of the diagonals.<BR>\n" );
document.write( "Mark an acute angle between the diagonals. It is 72°.<BR>\n" );
document.write( "Mark an obtuse angle between the diagonals. It is 180° - 72° = 108°.\r<BR>\n" );
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document.write( "Find the triangle formed by the halves of diagonals with the acute angle 72° between them.<BR>\n" );
document.write( "Apply the cosine theorem to this triangle.<BR>\n" );
document.write( "You will find one side of the parallelogram.\r<BR>\n" );
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document.write( "Find the other triangle formed by the halves of diagonals with the obtuse angle of 108° between them.<BR>\n" );
document.write( "Apply the cosine theorem to this triangle.<BR>\n" );
document.write( "You will find the other side of the parallelogram.\r<BR>\n" );
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document.write( "Notice that cos(108°) = -cos(72°).\r<BR>\n" );
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