document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113594>Question 113594</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132321025/algebrahomeworkh>Mathematics for the Trades</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 14. An oblique triangle has A=68 degrees, B= 79 degrees, and b= 8.0 ft. Determine the length of side c. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82717 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=82717\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An oblique triangle has:\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=68%B0 ALIGN=MIDDLE  ALT=\"A=68%B0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=+79%B0 ALIGN=MIDDLE  ALT=\"B=+79%B0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=+8.0+ft ALIGN=MIDDLE  ALT=\"b=+8.0+ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "\n" );
document.write( "Determine the length of 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" );
document.write( "\n" );
document.write( "The basic relationships among sides and angles of an oblique triangle are given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=the+_Law+_of_+Sines ALIGN=MIDDLE  ALT=\"the+_Law+_of_+Sines\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=the_+Law_+of_+Cosines ALIGN=MIDDLE  ALT=\"the_+Law_+of_+Cosines\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "\n" );
document.write( "When three parts (including a side) of an oblique triangle are given, the Law of Sines or the Law of Cosines can be used to solve the triangle.\r<BR>\n" );
document.write( "\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=four ALIGN=MIDDLE  ALT=\"four\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+possible ALIGN=MIDDLE  ALT=\"+possible\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cases ALIGN=MIDDLE  ALT=\"+cases\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "1. One side and two angles are given. <BR>\n" );
document.write( "2. Two sides and one opposite angle are given. <BR>\n" );
document.write( "3. Two sides and the included angle are given. <BR>\n" );
document.write( "4. Three sides are given. \r<BR>\n" );
document.write( "\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Law+ ALIGN=MIDDLE  ALT=\"Law+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=of ALIGN=MIDDLE  ALT=\"of\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Sines ALIGN=MIDDLE  ALT=\"+Sines\"   DISABLED_style= \"max-width:90%; height:auto;\" > is used in cases 1. and 2. <BR>\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Law ALIGN=MIDDLE  ALT=\"Law\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+of ALIGN=MIDDLE  ALT=\"+of\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Cosines ALIGN=MIDDLE  ALT=\"+Cosines\"   DISABLED_style= \"max-width:90%; height:auto;\" > is used in cases III and IV.\r<BR>\n" );
document.write( "\n" );
document.write( "LAW OF SINES <BR>\n" );
document.write( "For any triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC ALIGN=MIDDLE  ALT=\"ABC\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F+sin+A+=+b%2F+sin+B+=+c%2F+sin+C ALIGN=MIDDLE  ALT=\"a%2F+sin+A+=+b%2F+sin+B+=+c%2F+sin+C\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The sum of all angles is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%B0 ALIGN=MIDDLE  ALT=\"180%B0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and we will find third angle <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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+B+%2B+C+=+180%B0 ALIGN=MIDDLE  ALT=\"A+%2B+B+%2B+C+=+180%B0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=68+%2B+79+%2B+C+=+180 ALIGN=MIDDLE  ALT=\"68+%2B+79+%2B+C+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=147+%2B+C+=+180 ALIGN=MIDDLE  ALT=\"147+%2B+C+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+180++-+147 ALIGN=MIDDLE  ALT=\"C+=+180++-+147\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+33 ALIGN=MIDDLE  ALT=\"C+=+33\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2F+sin+C+=+b%2F+sin+B ALIGN=MIDDLE  ALT=\"c%2F+sin+C+=+b%2F+sin+B\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "	<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c++=+%28b%2F+sin+B%29+sin+C+ ALIGN=MIDDLE  ALT=\"c++=+%28b%2F+sin+B%29+sin+C+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c++=+%288ft%2F+sin+79%29+%28sin+33%29 ALIGN=MIDDLE  ALT=\"c++=+%288ft%2F+sin+79%29+%28sin+33%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "	<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%2879%29+=+0.98162718344766 ALIGN=MIDDLE  ALT=\"sin+%2879%29+=+0.98162718344766\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.98 ALIGN=MIDDLE  ALT=\"0.98\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2833%29+=+0.54463903501503 ALIGN=MIDDLE  ALT=\"sin%2833%29+=+0.54463903501503\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.54 ALIGN=MIDDLE  ALT=\"0.54\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "then\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c++=+%288.0ft%2F+0.98%29+%280.54%29 ALIGN=MIDDLE  ALT=\"c++=+%288.0ft%2F+0.98%29+%280.54%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c++=+%288.16ft%29%28+0.54%29 ALIGN=MIDDLE  ALT=\"c++=+%288.16ft%29%28+0.54%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c++=+4.4ft ALIGN=MIDDLE  ALT=\"c++=+4.4ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );