document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204634>Question 1204634</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 = 111°,<BR>\n" );
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document.write( "a = 12,<BR>\n" );
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document.write( "b = 23 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841026 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=841026\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "As mentioned by the other tutors, the <font color=red>triangle <u>cannot</u> be formed</font> with these sides and given angle. <BR>\n" );
document.write( "Using the argument \"largest side opposite largest angle\" is perhaps the most efficient pathway.\r<BR>\n" );
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document.write( "I'll show the law of sines scratch work that will lead to the same conclusion.\r<BR>\n" );
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document.write( "sin(alpha)/a = sin(beta)/b<BR>\n" );
document.write( "sin(111)/12 = sin(beta)/23<BR>\n" );
document.write( "sin(beta) = 23*sin(111)/12<BR>\n" );
document.write( "sin(beta) = 1.789 approximately <BR>\n" );
document.write( "Please make sure that your calculator is set to degrees mode.\r<BR>\n" );
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document.write( "We stop here since there are no real number solutions for angle beta. <BR>\n" );
document.write( "Recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%3C=+sin%28x%29+%3C=+1 ALIGN=MIDDLE  ALT=\"-1+%3C=+sin%28x%29+%3C=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The largest sine can get is 1.\r<BR>\n" );
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document.write( "Answer: <font color=red>impossible</font><BR>\n" );
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