document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=934849>Question 934849</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a triangle is 40 cm squared. Find the length of the side included between the angles A=30 degrees and B=50 degrees. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #567893 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=567893\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > = base of the triangle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > = altitude of the triangle\r<BR>\n" );
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document.write( "Area of a triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+%281%2F2%29bh+=40 ALIGN=MIDDLE  ALT=\"A=+%281%2F2%29bh+=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+2%2A40%2Fh ALIGN=MIDDLE  ALT=\"b+=+2%2A40%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+80%2Fh ALIGN=MIDDLE  ALT=\"b+=+80%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > ........eq. 1\r<BR>\n" );
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document.write( "Angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+180+-+30+-+50+=+100 ALIGN=MIDDLE  ALT=\"C+=+180+-+30+-+50+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the Law of Sines,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28100%29%2F%28AB%29+=+sin+%2850%29%2Fb ALIGN=MIDDLE  ALT=\"sin+%28100%29%2F%28AB%29+=+sin+%2850%29%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB ALIGN=MIDDLE  ALT=\"AB\"   DISABLED_style= \"max-width:90%; height:auto;\" > = length of the side included between the angles <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+30 ALIGN=MIDDLE  ALT=\"A+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=50 ALIGN=MIDDLE  ALT=\"B+=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving 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;\" >\",\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+%28AB%29%28sin+%2850%29%2Fsin+%28100%29%29 ALIGN=MIDDLE  ALT=\"b+=+%28AB%29%28sin+%2850%29%2Fsin+%28100%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ............eq. 2\r<BR>\n" );
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document.write( "Since eq.1 = eq.2, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%2Fh+=+%28AB%29%28sin+%2850%29%2Fsin+%28100%29%29 ALIGN=MIDDLE  ALT=\"80%2Fh+=+%28AB%29%28sin+%2850%29%2Fsin+%28100%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB ALIGN=MIDDLE  ALT=\"AB\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB+=+80%28sin+%28100%29%29%2F%28h%2Asin+%2850%29%29+.......eq.33%0D%0A%0D%0ALook+at+your+triangle+set-up+and+note+that%0D%0A%0D%0A%7B%7B%7Bsin+%2830%29+=+h%2FAB ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+AB%28sin+%2830%29%29+=+AB%2F2 ALIGN=MIDDLE  ALT=\"h+=+AB%28sin+%2830%29%29+=+AB%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+AB%2F2 ALIGN=MIDDLE  ALT=\"h+=+AB%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, substitute this in eq.3,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB+=+80%28sin+%28100%29%29%2F%28%28AB%2F2%29%2Asin%2850%29%29 ALIGN=MIDDLE  ALT=\"AB+=+80%28sin+%28100%29%29%2F%28%28AB%2F2%29%2Asin%2850%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB+=+2%2A80%28sin+%28100%29%29%2F%28AB%2Asin%2850%29%29 ALIGN=MIDDLE  ALT=\"AB+=+2%2A80%28sin+%28100%29%29%2F%28AB%2Asin%2850%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplifying the above,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AB%29%5E2+=+160%28sin+%28100%29%2Fsin+%2850%29%29 ALIGN=MIDDLE  ALT=\"%28AB%29%5E2+=+160%28sin+%28100%29%2Fsin+%2850%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AB%29%5E2+=+160%280.9848%2F0.7660%29 ALIGN=MIDDLE  ALT=\"%28AB%29%5E2+=+160%280.9848%2F0.7660%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AB%29%5E2+=+205.70 ALIGN=MIDDLE  ALT=\"%28AB%29%5E2+=+205.70\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB+=+14.34cm ALIGN=MIDDLE  ALT=\"AB+=+14.34cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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