document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=698781>Question 698781</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve triangle ABC, given A = 43 degrees, a = 13 and c = 16? Not sure how to figure out side b. The triangle is not a right angled triangle.\r<BR>\n" );
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document.write( "Thanks.<BR>\n" );
document.write( "Matt </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #431057 by </B><A HREF=/tutors/aboutme.mpl?userid=Simnepi><B>Simnepi(216)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Simnepi><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=Simnepi><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=431057\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You need to use the cosine rule, which is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+b%5E2+%2B+c%5E2+-+2%2Ab%2Ac%2ACosA ALIGN=MIDDLE  ALT=\"a%5E2+=+b%5E2+%2B+c%5E2+-+2%2Ab%2Ac%2ACosA\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute in the values for the variables to give<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%5E2+=+b%5E2+%2B+16%5E2+-+2%2Ab%2A16%2ACos43 ALIGN=MIDDLE  ALT=\"13%5E2+=+b%5E2+%2B+16%5E2+-+2%2Ab%2A16%2ACos43\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to give<BR>\n" );
document.write( "169 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 256 - 23.403*b<BR>\n" );
document.write( "rearranging gives<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 23.403b + 87 = 0 <BR>\n" );
document.write( "now if we let b = x we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 23.304x + 87 = 0<BR>\n" );
document.write( "Now we can solve this equation using the formula for quadratic solutions eg<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-23.403+%2B-+sqrt+%28-23.403%5E2+-+4%2A1%2A87%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-23.403+%2B-+sqrt+%28-23.403%5E2+-+4%2A1%2A87%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "calculating this gives us 2 values for x(b)<BR>\n" );
document.write( "these are x = 18.767 or x = 4.636 </SPAN>\n" );
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