document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=278282>Question 278282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello my teacher gave my class a worksheet with this problem: \r<BR>\n" );
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document.write( "The lengths of two sides of a parallelogram are 6 inches and 10 inches and the angle between them measures 41 degrees. What is the length of the altitude on the long side?\r<BR>\n" );
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document.write( "Thanks for any help.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854151 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53742)</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=854151\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Hello, my teacher gave my class a worksheet with this problem:<BR>\n" );
document.write( "The lengths of two sides of a parallelogram are 6 inches and 10 inches and the angle between them measures 41 degrees. <BR>\n" );
document.write( "What is the length of the altitude on the long side?<BR>\n" );
document.write( "Thanks for any help.<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This is a nice problem, and I will show you a remarkable method to solve it.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The solution and the answer in the post by @mananth are fatally incorrect.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is fatally incorrect, because both the guiding idea (the conception) and calculations are wrong.\r<BR>\n" );
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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;\">\r\n" );
document.write( "The idea is to use two different formulas for the area of the parallelogram.\r\n" );
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document.write( "One formula for the area of the parallelogram is\r\n" );
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document.write( "    area = a*b*sin(41°).     (1)  \r\n" );
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document.write( "It says that the area of the parallelogram is the product of its two adjacent sides by the sine of the angle between them.\r\n" );
document.write( "Another formula for the area of the parallelogram is\r\n" );
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document.write( "    area = a*h.             (2)\r\n" );
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document.write( "It says that the area of the parallelogram is the product of its base (one of the two adjacent sides)\r\n" );
document.write( "by the altitude of the parallelogram h.\r\n" );
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document.write( "Thus we equate right sides in formulas (1) and (2)\r\n" );
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document.write( "    a*b*sin(41°) = a*h.\r\n" );
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document.write( "We then cancel the common factor 'a', and we get\r\n" );
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document.write( "    h = b*sin(41°).    (3)\r\n" );
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document.write( "Now from (3) we get the value of 'h'\r\n" );
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document.write( "    h = b*sin(41°) = 6*0.65605902899 = 3.936 inches  (rounded).\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "At this point, the problem is solved completely and correctly,<BR>\n" );
document.write( "and you learned a new method for this problem.\r<BR>\n" );
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