document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=894333>Question 894333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle ABCD, which is 40 inches high by 20 wide, leans so that its top is 4 inches to the right of vertical.<BR>\n" );
document.write( "ie corner A (top left) is 4 inches to the right of corner D (bottom left).\r<BR>\n" );
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document.write( "By how much must I lift corner C to make the sides AD and BC vertical?<BR>\n" );
document.write( "(and how do you work it out accurately?)<BR>\n" );
document.write( "The answer will be about 2 inches but that's logic, not maths.\r<BR>\n" );
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document.write( "Thank you for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #541968 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=541968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your logic is correct.<BR>\n" );
document.write( "the solution is 2.\r<BR>\n" );
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document.write( "i solved it using trigonometry, but it was quite messy and required the use of the calculator.  the solution, however, turned out to be exactly 2.\r<BR>\n" );
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document.write( "i then looked at it geometrically and, while not obvious, it turns out that the triangles are similar and, since similar triangles have proportional sides, you get a ratio of x/20 = 4/40 and you wind up with x = 2, x being the height you are looking for.  in the diagram shown below, x represents the length of DB.\r<BR>\n" );
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document.write( "the geometric logic has to do with parallel lines and vertical angles and complementary angles.\r<BR>\n" );
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document.write( "it's a bit of a mish mash of geometric relationships.\r<BR>\n" );
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document.write( "the following diagram with all the angles that are equal to each other that matter to the solution is shown below.\r<BR>\n" );
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document.write( "look below the diagram for further comments.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/082202.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the bottom line on the geometric analysis is that triangle AFD is similar to triangle DGC because all their angles are equal.\r<BR>\n" );
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document.write( "since the triangles are similar, their corresponding sides are proportional.\r<BR>\n" );
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document.write( "FA is the side opposite angle FDA<BR>\n" );
document.write( "DG is the side opposite angle GCD\r<BR>\n" );
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document.write( "AD is the side opposite angle AFD<BR>\n" );
document.write( "DC is the side opposite angle DGC\r<BR>\n" );
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document.write( "their corresponding sides are proportional.\r<BR>\n" );
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document.write( "you get 4/40 = DG / 20\r<BR>\n" );
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document.write( "solve for DG and you get DG = 20*4/40 = 80/40 = 2\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "point C has to be raised up to the height of point D in order for the rectangle to be vertically aligned.\r<BR>\n" );
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document.write( "the height of point D from point G is equal to the length of DG which is equal to 2.\r<BR>\n" );
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document.write( "i didn't show you the trigonometric solution because it appears you are in a geometry course rather than a trigonometry course.\r<BR>\n" );
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document.write( "the trigonometry solution does confirm the geometric solution however, so no problem there.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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