document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969688>Question 969688</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An isoceles triangle has congruent sides that each measure 3 feet and a base angle of measure of x as shown in the sketch. The third side has a whole number length, if x <60 degrees , what are the possibilities of the perimeter of the triangle?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592490 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592490\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> v, the vertex angle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%2Bx%2Bx=180 ALIGN=MIDDLE  ALT=\"v%2Bx%2Bx=180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=180-2x ALIGN=MIDDLE  ALT=\"v=180-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "One objective is to find a formula for the base length.<BR>\n" );
document.write( "b, the length of the base.<BR>\n" );
document.write( "Law of Cosines:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2%2B3%5E3-2%2A3%2A3%2Acos%28v%29=b%5E2 ALIGN=MIDDLE  ALT=\"3%5E2%2B3%5E3-2%2A3%2A3%2Acos%28v%29=b%5E2\"   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=18-18%2Acos%28v%29=b%5E2 ALIGN=MIDDLE  ALT=\"18-18%2Acos%28v%29=b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=18-18%2Acos%28180-2x%29 ALIGN=MIDDLE  ALT=\"b%5E2=18-18%2Acos%28180-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----Think or inspect this angle on The Unit Circle.\r<BR>\n" );
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document.write( "....  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28180-2x%29=-cos%282x%29 ALIGN=MIDDLE  ALT=\"cos%28180-2x%29=-cos%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Revise the equation for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=18%2B18%2Acos%282x%29 ALIGN=MIDDLE  ALT=\"b%5E2=18%2B18%2Acos%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The isosceles triangle to have any meaning and match the given requirement,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3Cx%3C60 ALIGN=MIDDLE  ALT=\"0%3Cx%3C60\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Perimeter:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Bsqrt%2818%2B18%2Acos%280%29%29%3Eperimeter%3E6%2Bsqrt%2818%2B18cos%28120%29%29 ALIGN=MIDDLE  ALT=\"6%2Bsqrt%2818%2B18%2Acos%280%29%29%3Eperimeter%3E6%2Bsqrt%2818%2B18cos%28120%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Bsqrt%2818%2B18%2A1%29%3Eperimeter%3E6%2Bsqrt%2818%2B18%2A%28-cos%2860%29%29%29 ALIGN=MIDDLE  ALT=\"6%2Bsqrt%2818%2B18%2A1%29%3Eperimeter%3E6%2Bsqrt%2818%2B18%2A%28-cos%2860%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, again refer to Unit Circle to see.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Bsqrt%2836%29%3Eperimeter%3E6%2Bsqrt%2818%2B18%2A%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"6%2Bsqrt%2836%29%3Eperimeter%3E6%2Bsqrt%2818%2B18%2A%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%3Eperimeter%3E6%2Bsqrt%2827%29 ALIGN=MIDDLE  ALT=\"12%3Eperimeter%3E6%2Bsqrt%2827%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2812%3Eperimeter%3E6%2B3%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"highlight%2812%3Eperimeter%3E6%2B3%2Asqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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