document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29865>Question 29865</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm trying to generate Penrose tiling in Photoshop.  To get my rhomb shapes accurate I need to know the following.\r<BR>\n" );
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document.write( "I skew a square of 400 units by 400 units to form a parallelogram with angles 72, 108, 72, 108.  I know the angles I'm aiming for but the only input data in Photoshop is the distance I push the square along the X axis.\r<BR>\n" );
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document.write( "As far as I can tell I could use Pythagoras theorem to calculate the length a by knowing that a right angle triangle is formed with an angle of 18 degrees as I push the square to form the angle of 72 degrees.\r<BR>\n" );
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document.write( "I think I calculated that the length of the hypotenuse would have to be sqrt of 400squared by 400 squared ie 566.\r<BR>\n" );
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document.write( "I pretty  much failed maths at school and it's taken me hours to get this far.  I'm stumped when I start reading about finding the length of a leg based on the angle when I didn't even know what cosecant was.\r<BR>\n" );
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document.write( "I'd like to understand this, not just have the answer, because I'm sure that I will be needing to redo the calculation to make my 'thin rhomb' and if I continue an interest in tesselation art this is going to be a regular need.\r<BR>\n" );
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document.write( "Many thanks if you can help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #16637 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=16637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If I get the picture correctly, you are trying to create a rhomb(sic) (in the U.S. this is called a rhombus) by skewing a 400 X 400-unit square so that the interior angles of the rhombus are: 72, 108, 72, and 108 degrees.\r<BR>\n" );
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document.write( "Let's assume that your initial square is based on the x-axis and the left<BR>\n" );
document.write( "side is coincident with the y-axis, so the bottom-left corner is located at the origin of the coordiante system.\r<BR>\n" );
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document.write( "Now you'll displace the top of the square some distance to the right in the x-direction, leaving the bottom fixed of course. Your question is: What should the displacement distance be to obtain the required rhombus?\r<BR>\n" );
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document.write( "After the displacement, if you drop a perpendicular line from the top-left corner of the newly-formed rhombus to the base, you will have formed a right-triangle whose hypotenuse (h) is the length of the original square (400 units) and whose base angle is 72 degrees.\r<BR>\n" );
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document.write( "You can find the displacement distance (d) using the cosine of 72 degrees. Recall that the cosine of the angle of interest is:<BR>\n" );
document.write( "Cosine = (side adjacent to the angle)/(the hypotenuse). The side adjacent is the displacent (d). So: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2872%29+=+d%2Fh ALIGN=MIDDLE  ALT=\"cos%2872%29+=+d%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > But h = 400<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2872%29+=+d%2F400 ALIGN=MIDDLE  ALT=\"cos%2872%29+=+d%2F400\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for d.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+400cos%2872%29 ALIGN=MIDDLE  ALT=\"d+=+400cos%2872%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+123.606 ALIGN=MIDDLE  ALT=\"d+=+123.606\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The required displacement is 123.6 units (rounded to the nearest tenth) </SPAN>\n" );
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