document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180768>Question 1180768</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In describing her plot of land to the surveyor Jemma  provided the following details: One side is lined by a   40m fence. Another side runs parallel to the road for 22meters. Those two sides create a   30 degree angle between them. The inspector says this information can create 2 different triangular plots of land. Show work to calculate the remaining angles and the third side of the triangle for both possible plots of land. Round your measurements to the tenths place.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810565 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52799)</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=810565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "It is true that in &nbsp;Geometry there is only one triangle with two given sides and the concluded angle given.\r<BR>\n" );
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document.write( "All other triangles are &nbsp;CONGRUENT &nbsp;to this triangle.\r<BR>\n" );
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document.write( "It means that all other congruent triangles can be over-imposed using translations, rotations &nbsp;AND/OR &nbsp;mirror reflections.\r<BR>\n" );
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document.write( "So, &nbsp;from the Geometry point of view, &nbsp;all these triangles are equivalent.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;But living on the Earth surface, &nbsp;we can only move triangles, using \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;translations and/or rotations - we &nbsp;CAN &nbsp;NOT &nbsp;make a &nbsp;MIRROR &nbsp;REFLECTION, &nbsp;in fact.\r<BR>\n" );
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document.write( "It is why in this scenario the inspector says that &nbsp;TWO &nbsp;DIFFERENT &nbsp;triangle plots are possible, &nbsp;based on given description.\r<BR>\n" );
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document.write( "If you imagine that the road is in &nbsp;West-East direction and the plot is on the &nbsp;North side of the road,\r<BR>\n" );
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document.write( "then one plot can be presented by a triangle skewed &nbsp;West, &nbsp;while another plot can be presented by a triangle skewed &nbsp;East.\r<BR>\n" );
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document.write( "Although the triangles are &nbsp;CONGRUENT &nbsp;and are non-distinguishable from the formal &nbsp;Geometry point of view,\r<BR>\n" );
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document.write( "NETHERVELESS &nbsp;they are different on the &nbsp;Earth surface and &nbsp;CAN &nbsp;NOT &nbsp;be overposed by translations and rotations,\r<BR>\n" );
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document.write( "since they are mirror images one to another.\r<BR>\n" );
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document.write( "At this point I complete my explanation about the different plots - on the &nbsp;Earth surface they are really different and \r<BR>\n" );
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document.write( "can not be overposed by translations and rotations.\r<BR>\n" );
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document.write( "Regarding calculation the third side of the triangle, &nbsp;use the &nbsp;Cosine Law.\r<BR>\n" );
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document.write( "Regarding finding two other angles of triangles, &nbsp;use the &nbsp;Sine Law.\r<BR>\n" );
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document.write( "-------------\r<BR>\n" );
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document.write( "Have a nice day and enjoy my explanation &nbsp;(!)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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