document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=919179>Question 919179</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two sides an angle of a triangle are given, determine whether the given measurements produce one triangle, two triangles or no triangle at all.\r<BR>\n" );
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document.write( "a = 10 b = 9 A = 30 degrees\r<BR>\n" );
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document.write( "(Im very stuck on this problem and the choices they give us is like B = what or C = and also C1 and B1 etc.\r<BR>\n" );
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document.write( "please help!\r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #557588 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=557588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Having the measures of one angle and the opposite side, you can use law of sines to try to solve the triangle.<BR>\n" );
document.write( "In this case, you can use A, a and b to find B, C and c).<BR>\n" );
document.write( "Law of sines says that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29%2Fa=sin%28B%29%2Fb ALIGN=MIDDLE  ALT=\"sin%28A%29%2Fa=sin%28B%29%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2830%5Eo%29%2F10=sin%28B%29%2F9 ALIGN=MIDDLE  ALT=\"sin%2830%5Eo%29%2F10=sin%28B%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5%2F10=sin%28B%29%2F9 ALIGN=MIDDLE  ALT=\"0.5%2F10=sin%28B%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A0.5%2F10=sin%28B%29 ALIGN=MIDDLE  ALT=\"9%2A0.5%2F10=sin%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28B%29=0.45 ALIGN=MIDDLE  ALT=\"sin%28B%29=0.45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28B=26.74%5Eo%29 ALIGN=MIDDLE  ALT=\"highlight%28B=26.74%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded).<BR>\n" );
document.write( "That is the only possible measure for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the only possible triangle with the given measurements.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28180%5Eo-26.74%5Eo%29=sin%28153.26%5Eo%29=0.45 ALIGN=MIDDLE  ALT=\"sin%28180%5Eo-26.74%5Eo%29=sin%28153.26%5Eo%29=0.45\"   DISABLED_style= \"max-width:90%; height:auto;\" > too,<BR>\n" );
document.write( "but you could not have angles measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5Eo ALIGN=MIDDLE  ALT=\"30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=153.26%5Eo ALIGN=MIDDLE  ALT=\"153.26%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the same triangle,<BR>\n" );
document.write( "because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5Eo%2B153.26%5Eo=183.26%5Eo%3E180%5Eo ALIGN=MIDDLE  ALT=\"30%5Eo%2B153.26%5Eo=183.26%5Eo%3E180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So there is only one option, one triangle,<BR>\n" );
document.write( "just one <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > and one <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > , no <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B1 ALIGN=MIDDLE  ALT=\"B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C1 ALIGN=MIDDLE  ALT=\"C1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=180%5Eo-%28A%2BB%29 ALIGN=MIDDLE  ALT=\"C=180%5Eo-%28A%2BB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=180%5Eo-%2830%5Eo%2B26.74%5Eo%29 ALIGN=MIDDLE  ALT=\"C=180%5Eo-%2830%5Eo%2B26.74%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=180%5Eo-56.74%5Eo ALIGN=MIDDLE  ALT=\"C=180%5Eo-56.74%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C=123.26%5Eo%29 ALIGN=MIDDLE  ALT=\"highlight%28C=123.26%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded).<BR>\n" );
document.write( "Law of sines also says <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29%2Fa=sin%28C%29%2Fc ALIGN=MIDDLE  ALT=\"sin%28A%29%2Fa=sin%28C%29%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fsin%28A%29=c%2Fsin%28C%29 ALIGN=MIDDLE  ALT=\"a%2Fsin%28A%29=c%2Fsin%28C%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=10%2F0.5=c%2Fsin%28123.26%5Eo%29 ALIGN=MIDDLE  ALT=\"10%2F0.5=c%2Fsin%28123.26%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20=c%2F0.8362 ALIGN=MIDDLE  ALT=\"20=c%2F0.8362\"   DISABLED_style= \"max-width:90%; height:auto;\" >(rounded)--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=20%2A0.8362 ALIGN=MIDDLE  ALT=\"c=20%2A0.8362\"   DISABLED_style= \"max-width:90%; height:auto;\" >(rounded)--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=16.7%29 ALIGN=MIDDLE  ALT=\"highlight%28c=16.7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded).<BR>\n" );
document.write( " <BR>\n" );
document.write( "When you draw the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5Eo ALIGN=MIDDLE  ALT=\"30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > angle, you can locate<BR>\n" );
document.write( "point A, at the vertex of the angle,<BR>\n" );
document.write( "ray AB on one side of the angle,<BR>\n" );
document.write( "and point C, at distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=9 ALIGN=MIDDLE  ALT=\"b=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > from A on the other side of the angle (side AC).<BR>\n" );
document.write( "You know that point B is at distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=10 ALIGN=MIDDLE  ALT=\"a=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > from point C,<BR>\n" );
document.write( "and that it is on ray AB,<BR>\n" );
document.write( "so you just draw an arc with radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=10 ALIGN=MIDDLE  ALT=\"a=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > centered at point C.<BR>\n" );
document.write( "The point where that arc intersects ray AB is point B.<BR>\n" );
document.write( "angle<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C150%2C-1%2C19%2C-2%2C5.5%2C%0D%0Aarrow%280%2C0%2C18.9%2C0%29%2Cline%280%2C0%2C7.79%2C4.5%29%2Clocate%287.7%2C5.2%2CC%29%2C%0D%0Agreen%28arc%287.79%2C4.5%2C20%2C20%2C-10%2C40%29%29%2Clocate%2812.5%2C5%2Cgreen%2810%29%29%2C%0D%0Agreen%28arrow%2813.5%2C4.5%2C17.79%2C4.5%29%29%2Cgreen%28arrow%2812.5%2C4.5%2C7.79%2C4.5%29%29%2C%0D%0Alocate%28-0.4%2C0%2CA%29%2Clocate%281.1%2C1.2%2Cred%2830%5Eo%29%29%2C%0D%0Ared%28arc%280%2C0%2C5%2C5%2C-30%2C0%29%29%2Clocate%284%2C2.5%2Cb=9%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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