document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105678>Question 1105678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Describe how the Law of Cosines can be used to solve the ambiguous case of the oblique triangle ABC, where a = 12 feet, b = 30 feet, and A = 20°. Is the result the same as when the Law of Sines is used to solve the triangle? Describe the advantages and the disadvantages of each method. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #720559 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=720559\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Describe how the Law of Cosines can be used to solve the ambiguous case of the oblique triangle ABC, where a = 12 feet, b = 30 feet, and A = 20°. Is the result the same as when the Law of Sines is used to solve the triangle? Describe the advantages and the disadvantages of each method. <BR>\n" );
document.write( "Using Law of Sines::<BR>\n" );
document.write( "sin(B)/b = sin(A)/a<BR>\n" );
document.write( "----<BR>\n" );
document.write( "sin(B) = 30[sin(20)/12] = 0.86<BR>\n" );
document.write( "B = arcsin(0.86) = 58.77 degrees<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Then C = 180 - (20+58.77) = 101.23<BR>\n" );
document.write( "Then c = sin(C)[12/sin(20)] = 34.41<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Using Law of Cosines::<BR>\n" );
document.write( "c^2 = a^2 + b^2-2ab*cos(C)<BR>\n" );
document.write( "But we don't know \"c\" or \"C\"<BR>\n" );
document.write( "---<BR>\n" );
document.write( "So we have to use::<BR>\n" );
document.write( "12^2 = 30^2 + c^2 - 2*30c*cos(20)<BR>\n" );
document.write( "144 = 900 + c^2 - 60c*0.9397<BR>\n" );
document.write( "This is a quadratic in \"c\" and will have two solutions.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "You would then have to find the two values of \"c\".<BR>\n" );
document.write( "Then find the two angles.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Looks like first using Law of Sines would be more direct.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "------------ \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );