document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=197170>Question 197170</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the measures of the angles of a rhombus ABCD of side 5m and whose longest diagonal is 8m? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147821 by </B><A HREF=/tutors/aboutme.mpl?userid=J2R2R><B>J2R2R(94)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=J2R2R><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=J2R2R><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=147821\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have a triangle made from of two sides of the rhombus AB and BC equal to 5cm and the diagonal AC equal to 8cm.\r<BR>\n" );
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document.write( "The Cosine Rule for triangle ABC states\r<BR>\n" );
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document.write( "AC^2 = AB^2 + BC^2 - 2 AB BC cos ABC\r<BR>\n" );
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document.write( "Therefore\r<BR>\n" );
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document.write( "64 = 25 + 25 - 50 cos ABC	\r<BR>\n" );
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document.write( "64 = 50 - 50 cos ABC\r<BR>\n" );
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document.write( "14 = - 50 cos ABC\r<BR>\n" );
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document.write( "-7/25 = cos ABC\r<BR>\n" );
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document.write( "Angle ABC = approx 106.3 degrees as is the opposite angle CDA of the rhombus.\r<BR>\n" );
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document.write( "The other two angles BCA and CAB of the triangle (isosceles) are equal and half the angle made in the corner by the rhombus since a triangle on one side of a diagonal of a rhombus is a mirror image of the triangle on the other side of the diagonal.\r<BR>\n" );
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document.write( "Alternatively you could say that since the opposite sides of a rhombus are parallel then adjacent angles add up to 180 degrees and opposite angles are equal.\r<BR>\n" );
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document.write( "Thus angles DAB and BCD are approximately 180 – 106.3 = 73.7 degrees. </SPAN>\n" );
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