document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1075746>Question 1075746</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two sides and an angle are given below.  Determine whether the given information results in one&#8203; triangle, two&#8203; triangles, or no triangle at all.  Solve any&#8203; triangle(s) that results.<BR>\n" );
document.write( "b=4,c=5,B=40 degrees </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #690393 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=690393\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you draw AB and angle B,<BR>\n" );
document.write( "you realize that there are two possible locations for point C,<BR>\n" );
document.write( "at a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > from A.<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282%29 ALIGN=MIDDLE  ALT=\"highlight%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > triangles. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C250%2C-0.5%2C5.5%2C-0.4%2C4.6%2C%0D%0Agreen%28triangle%280%2C0%2C5%2C0%2C3.89%2C0.931%29%29%2C%0D%0Ared%28triangle%280%2C0%2C5%2C0%2C0.242%2C3.993%29%29%2C%0D%0Aline%280%2C0%2C5%2C0%29%2Cline%285%2C0%2C-0.362%2C4.5%29%2C%0D%0Aarrow%285%2C0%2C-0.362%2C4.5%29%2Clocate%28-0.1%2C0%2CA%29%2C%0D%0Alocate%285%2C0%2CB%29%2Clocate%283.9%2C1.15%2Cgreen%28C%29%29%2C%0D%0Alocate%280.35%2C4.2%2Cred%28C%29%29%2Carc%285%2C0%2C2%2C2%2C180%2C220%29%2C%0D%0Alocate%283.5%2C0.6%2C40%5Eo%29%2Carc%280%2C0%2C8%2C8%2C260%2C350%29%2C%0D%0Alocate%282.5%2C0%2C5%29%2Clocate%280.2%2C2%2Cred%284%29%29%2C%0D%0Alocate%282%2C0.8%2Cgreen%284%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Law of sines says that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2840%5Eo%29%2F4=sin%28C%29%2F5 ALIGN=MIDDLE  ALT=\"sin%2840%5Eo%29%2F4=sin%28C%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28C%29=about0.80348 ALIGN=MIDDLE  ALT=\"sin%28C%29=about0.80348\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28red%28C%29=53.464%5Eo%2C%22or%22%2Cgreen%28C%29=126.536%5Eo%29 ALIGN=MIDDLE  ALT=\"system%28red%28C%29=53.464%5Eo%2C%22or%22%2Cgreen%28C%29=126.536%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28red%29 ALIGN=MIDDLE  ALT=\"red%28red%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > option,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=180%5Eo-40%5Eo-53.464%5Eo=86.536%5Eo ALIGN=MIDDLE  ALT=\"A=180%5Eo-40%5Eo-53.464%5Eo=86.536%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then, using law of shines again,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fsin%28A%29=b%2Fsin%28B%29 ALIGN=MIDDLE  ALT=\"a%2Fsin%28A%29=b%2Fsin%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , with approximate values becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F0.998173=4%2F0.642788 ALIGN=MIDDLE  ALT=\"a%2F0.998173=4%2F0.642788\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6.212 ALIGN=MIDDLE  ALT=\"a=6.212\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28green%29 ALIGN=MIDDLE  ALT=\"green%28green%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > option,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=180%5Eo-40%5Eo-126.536%5Eo=13.464%5Eo ALIGN=MIDDLE  ALT=\"A=180%5Eo-40%5Eo-126.536%5Eo=13.464%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4%2A0.23834%2F0.642788=1.449 ALIGN=MIDDLE  ALT=\"a=4%2A0.23834%2F0.642788=1.449\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );