document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193069>Question 193069</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In triangle ABC, a=6, b=7, and cos C=1/4\r<BR>\n" );
document.write( "\n" );
document.write( "A.) Find the exact area of the triangle. <BR>\n" );
document.write( "B.) Find C<BR>\n" );
document.write( "C.) Find sin A in simplest radical form.\r<BR>\n" );
document.write( "\n" );
document.write( "The part I'm having trouble with it what does cos C=1/4 mean? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144917 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20063)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=144917\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In triangle ABC, a=6, b=7, and cos C=1/4\r<BR>\n" );
document.write( "\n" );
document.write( "A.) Find the exact area of the triangle. <BR>\n" );
document.write( "B.) Find C<BR>\n" );
document.write( "C.) Find sin A in simplest radical form.\r<BR>\n" );
document.write( "\n" );
document.write( "The part I'm having trouble with it what does cos C=1/4 mean?\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%28C%29=1%2F4 ALIGN=MIDDLE  ALT=\"Cos%28C%29=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > means that the cosine of C is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The formula for the area is\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%28ab%2ASin%28C%29%29%2F2 ALIGN=MIDDLE  ALT=\"A+=+%28ab%2ASin%28C%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "So first we must find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28C%29 ALIGN=MIDDLE  ALT=\"sin%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28C%29 ALIGN=MIDDLE  ALT=\"cos%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "To do this we make use of the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sin%5E2alpha%2BCos%5E2alpha=1 ALIGN=MIDDLE  ALT=\"Sin%5E2alpha%2BCos%5E2alpha=1\"   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%5E2C%2BCos%5E2C=1 ALIGN=MIDDLE  ALT=\"Sin%5E2C%2BCos%5E2C=1\"   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%5E2C=1-Cos%5E2C ALIGN=MIDDLE  ALT=\"Sin%5E2C=1-Cos%5E2C\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Since we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%28C%29=1%2F4 ALIGN=MIDDLE  ALT=\"Cos%28C%29=1%2F4\"   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%5E2C=1-%281%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"Sin%5E2C=1-%281%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sin%5E2C=1-1%2F16 ALIGN=MIDDLE  ALT=\"Sin%5E2C=1-1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sin%5E2C=16%2F16-1%2F16 ALIGN=MIDDLE  ALT=\"Sin%5E2C=16%2F16-1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sin%5E2C=15%2F16 ALIGN=MIDDLE  ALT=\"Sin%5E2C=15%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sin%28C%29=sqrt%2815%2F16%29 ALIGN=MIDDLE  ALT=\"Sin%28C%29=sqrt%2815%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sin%28C%29=sqrt%2815%29%2F4 ALIGN=MIDDLE  ALT=\"Sin%28C%29=sqrt%2815%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now we can substitute in the area formula:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%28a%2Ab%2ASin%28C%29%29%2F2 ALIGN=MIDDLE  ALT=\"A+=+%28a%2Ab%2ASin%28C%29%29%2F2\"   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+=+%286%2A7%2A%28sqrt%2815%29%2F4%29%29%2F2 ALIGN=MIDDLE  ALT=\"A+=+%286%2A7%2A%28sqrt%2815%29%2F4%29%29%2F2\"   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+=+%286%2A7%2A%28sqrt%2815%29%2F4%29%29%2A%282%2F1%29 ALIGN=MIDDLE  ALT=\"A+=+%286%2A7%2A%28sqrt%2815%29%2F4%29%29%2A%282%2F1%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=A=%286%2A7%2A2%2F4%29sqrt%2815%29 ALIGN=MIDDLE  ALT=\"A=%286%2A7%2A2%2F4%29sqrt%2815%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=A=21sqrt%2815%29 ALIGN=MIDDLE  ALT=\"A=21sqrt%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Edwin </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );