document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201469>Question 1201469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the following problems. Show solutions and illustrate the given.<BR>\n" );
document.write( "1. A parallelogram has sides 15 cm and 25 cm and their included angle is <BR>\n" );
document.write( "740<BR>\n" );
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document.write( "I. Find its area.<BR>\n" );
document.write( "II. Find the lengths of the diagonals.<BR>\n" );
document.write( "III. Find the angle of intersection between diagonals. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835941 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "to find the area of parallelogram with 2 sides and an angle use formula<BR>\n" );
document.write( "Area = ab sin <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28theta%29 ALIGN=MIDDLE  ALT=\"%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Side 1 15 cm<BR>\n" );
document.write( "side 2 25 cm<BR>\n" );
document.write( "included angle =74 deg<BR>\n" );
document.write( "A = 15 * 25 * sin 74 degrees<BR>\n" );
document.write( "=360.47 cm^2<BR>\n" );
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document.write( "To find the third side of a triangle ( Here diagonal of parallelogram) given two sides and an angle. You use the cosine formula. If the three sides of the triangle are a, b and c and the angle between a and b is C, then c² = a² + b² - 2ab×cos C.\r<BR>\n" );
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document.write( "c = sqrt(15^2+25^2 - 2*15*25*cos 74 degrees)<BR>\n" );
document.write( "c=25.36 cm\r<BR>\n" );
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document.write( "Sum of adjacent angles of parallelogram are supplementary\r<BR>\n" );
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document.write( "The other angle is 180-74 = 106 deg<BR>\n" );
document.write( "Apply same formuala to get the other diagonal<BR>\n" );
document.write( "32.507 cm<BR>\n" );
document.write( "The diagonals bisect each other. So we can find the angle using the above formula. we can find the angle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=mananth&illustration_name=parallelogram_1.png\">.<BR>\n" );
document.write( "25<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );