document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204422>Question 1204422</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume 𝛼 is opposite side a, 𝛽 is opposite side b, and 𝛾 is opposite side c. Determine whether there is no triangle, one triangle, or two triangles. Then solve each triangle, if possible. Round each answer to the nearest tenth. (If not possible, enter IMPOSSIBLE.)<BR>\n" );
document.write( "𝛼 = 119°, <BR>\n" );
document.write( "a = 13,<BR>\n" );
document.write( " b = 27 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840656 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840656\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "if<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha+=+119 ALIGN=MIDDLE  ALT=\"alpha+=+119\"   DISABLED_style= \"max-width:90%; height:auto;\" >°,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+13 ALIGN=MIDDLE  ALT=\"a+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+27 ALIGN=MIDDLE  ALT=\"b+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha+%3E+90 ALIGN=MIDDLE  ALT=\"alpha+%3E+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >°, use the Law of Cosines equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=b%5E2%2Bc%5E2-2bc%2Acos%28alpha%29 ALIGN=MIDDLE  ALT=\"a%5E2=b%5E2%2Bc%5E2-2bc%2Acos%28alpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%5E2=27%5E2%2Bc%5E2-2%2A27c%2Acos%28119%29 ALIGN=MIDDLE  ALT=\"13%5E2=27%5E2%2Bc%5E2-2%2A27c%2Acos%28119%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=169=729%2Bc%5E2-54c%2Acos%28119%29 ALIGN=MIDDLE  ALT=\"169=729%2Bc%5E2-54c%2Acos%28119%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+%2B+54c%2Asin%28%2829pi%29%2F180%29+%2B+560+=+0 ALIGN=MIDDLE  ALT=\"c%5E2+%2B+54c%2Asin%28%2829pi%29%2F180%29+%2B+560+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+%2B+26.179c%2B560=0 ALIGN=MIDDLE  ALT=\"c%5E2+%2B+26.179c%2B560=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using quadratic formula, we get following solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+-13.0895+-+19.7146+%2Ai ALIGN=MIDDLE  ALT=\"c+=+-13.0895+-+19.7146+%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+-13.0895%2B+19.7146%2A+i ALIGN=MIDDLE  ALT=\"c+=+-13.0895%2B+19.7146%2A+i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, there is no real solution for side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ASS ALIGN=MIDDLE  ALT=\"ASS\"   DISABLED_style= \"max-width:90%; height:auto;\" > (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SSA ALIGN=MIDDLE  ALT=\"SSA\"   DISABLED_style= \"max-width:90%; height:auto;\" >) theorem with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha+%3E=+90 ALIGN=MIDDLE  ALT=\"alpha+%3E=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >° (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha+%3E=+pi%2F2 ALIGN=MIDDLE  ALT=\"alpha+%3E=+pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3C=+b ALIGN=MIDDLE  ALT=\"a+%3C=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no ALIGN=MIDDLE  ALT=\"no\"   DISABLED_style= \"max-width:90%; height:auto;\" > solutions and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no ALIGN=MIDDLE  ALT=\"no\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+triangle ALIGN=MIDDLE  ALT=\"+triangle\"   DISABLED_style= \"max-width:90%; height:auto;\" >!\r<BR>\n" );
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document.write( "answer:  IMPOSSIBLE\r<BR>\n" );
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