document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=450961>Question 450961</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the area of a parallelogram with diagonals of lengths 10 inches and 22 inches that intersect at a 65 degrees angle  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #310184 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=310184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The other tutor's solution is correct, but there is a faster way to find the area. Given the parallelogram (I have used the other tutor's as a reference),\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C550%2F3%2C-2%2C22%2C-2%2C9%2C%0D%0Alocate%288.2%2C4.3%2C%2265%B0%22%29%2C+locate%289%2C6%2C5%29%2C%0D%0Aline%280%2C0%2C13.87400479%2C0%29%2C%0D%0Aline%2813.87400479%2C0%2C20.79342001%2C7.185658223%29%2C%0D%0Aline%286.91941522%2C7.185658223%2C20.79342001%2C7.185658223%29%2C%0D%0Aline%286.91941522%2C7.185658223%2C0%2C0%29%2C%0D%0Aline%280%2C0%2C20.79342001%2C7.185658223%29%2C%0D%0Aline%286.91941522%2C7.185658223%2C13.87400479%2C0%29%2C%0D%0Alocate%286%2C2.1%2C11%29%2C+locate%2811.2%2C2%2C5%29%2C%0D%0Alocate%2813.5%2C4.5%2C11%29%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We see that the parallelogram is consisted of:\r<BR>\n" );
document.write( "\n" );
document.write( "*Two triangles with sides 5, 11, and a 65 degree angle in between<BR>\n" );
document.write( "*Two triangles with sides 5, 11, and a 115 degree angle in between\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you know the area of the triangle can be expressed as\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A = \frac{1}{2}ab \sin{\gamma}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\gamma\"> is the angle in between a and b, we can find the area of the parallelogram (denoted <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?A_p\"> this way. Here, we have two of each triangle, so\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A_p = 2(\frac{1}{2}(5)(11)\sin{(65)}) + 2(\frac{1}{2} (5)(11)\sin{(115)})\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A_p = 55\sin(65) + 55\sin(115)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Noting that sin(x) = sin(180-x), this is equal to\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A_p = 55\sin(65) + 55\sin(65) = 110\sin(65) = 99.694\"> (sq in) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );