document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122326>Question 1122326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diagonal of a parallelogram is 44.32 cm long and forms angles of 30°15' and 33°12' with the sides. Find the lengths of the two sides. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #738437 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10555)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=738437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The diagonal of a parallelogram is 44.32 cm long and forms angles of 30°15' and 33°12' with the sides. Find the lengths of the two sides.<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28matrix%281%2C4%2C+30%5Eo%2C+%2215%27%22%2C+%22=%22%2C+30.25%5Eo%29%2C+and%2C+matrix%281%2C4%2C+33%5Eo%2C+%2212%27%22%2C+%22=%22%2C+33.2%5Eo%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r\n" );
document.write( "Use one of the parallelogram's 2 triangles formed from drawing the diagonal, and law of sines to find the SHORTER side of the parallelogram.\r\n" );
document.write( "The equation for this is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C3%2C+44.32%2Fsin+%28116.55%5Eo%29%2C+%22=%22%2C+matrix%281%2C2%2C+Shorter%2C+side%29%2Fsin+%2830.25%5Eo%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >. This should give you  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28matrix%281%2C2%2C+24.959%2C+cm%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28matrix%281%2C2%2C+24.959%2C+cm%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the SHORTER side.\r\n" );
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document.write( "Use one of the parallelogram's 2 triangles formed from drawing the diagonal, and law of sines to find the LONGER side of the parallelogram. \r\n" );
document.write( "The equation for this is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C3%2C+44.32%2Fsin+%28116.55%5Eo%29%2C+%22=%22%2C+matrix%281%2C2%2C+Longer%2C+side%29%2Fsin+%2833.2%5Eo%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >. This should give you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28matrix%281%2C2%2C+27.129%2C+cm%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28matrix%281%2C2%2C+27.129%2C+cm%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the LONGER side.\r\n" );
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document.write( "These are the CORRECT lengths of the sides!</PRE> </SPAN>\n" );
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