document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198347>Question 1198347</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether it is possible to draw a triangle<BR>\n" );
document.write( " given each set of information. Sketch all possible<BR>\n" );
document.write( " triangles where appropriate. Calculate, then label, all<BR>\n" );
document.write( " side lengths to the nearest tenth of a centimetre and<BR>\n" );
document.write( " all angles to the nearest degree. <BR>\n" );
document.write( "b=12.2cm, c=8.2cm, AngleC=34 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831934 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=831934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let's see if we can use the Law of Sines to determine angle B.<BR>\n" );
document.write( "sin(B)/b = sin(C)/c<BR>\n" );
document.write( "sin(B)/12.2 = sin(34)/8.2<BR>\n" );
document.write( "sin(B) = 12.2*sin(34)/8.2<BR>\n" );
document.write( "sin(B) = 0.8319699<BR>\n" );
document.write( "B = arcsin(0.8319699) or B = 180-arcsin(0.8319699)<BR>\n" );
document.write( "B = 56.3016 or B = 123.6984<BR>\n" );
document.write( "These values are approximate.\r<BR>\n" );
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document.write( "If B = 56.3016, then<BR>\n" );
document.write( "A+B+C = 180<BR>\n" );
document.write( "A = 180-B-C<BR>\n" );
document.write( "A = 180-56.3016-34<BR>\n" );
document.write( "A = 89.6984<BR>\n" );
document.write( "which is a valid angle measure since 0 < A < 180.\r<BR>\n" );
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document.write( "If B = 123.6984, then<BR>\n" );
document.write( "A+B+C = 180<BR>\n" );
document.write( "A = 180-B-C<BR>\n" );
document.write( "A = 180-123.6984-34<BR>\n" );
document.write( "A = 22.3016<BR>\n" );
document.write( "which is also valid.\r<BR>\n" );
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document.write( "We have the SSA ambiguous case here, where we have 2 possible triangles. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/0fhqBTG.png\"><BR>\n" );
document.write( "Angle A could be 22.3016° marked in blue, or it could be 89.6984° marked in red.<BR>\n" );
document.write( "B1 and B2 represent possible locations for point B.<BR>\n" );
document.write( "Here's what it looks like to split the triangles up, to get a better look at them.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"70%\" src = \"https://i.imgur.com/40KQqt6.png\"><BR>\n" );
document.write( "I've also erased the \"1\" and \"2\" from \"B1\" and \"B2\" respectively.\r<BR>\n" );
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document.write( "I'll let you use the law of sines to determine the missing side for each possible triangle.<BR>\n" );
document.write( "I'll also let you round the angle measures to the nearest whole degree.<BR>\n" );
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