document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=924424>Question 924424</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if the vertex of an isosceles triangle is 80 degrees and the side opposite the vertex measures 12 cm, determine the perimeter of the triangle.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #560830 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=560830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  you can solve it this way:\r<BR>\n" );
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document.write( "An isosceles triangle can be considered as two right angle triangles joined together so use the tangent ratio to find its altitude <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "given angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=80 ALIGN=MIDDLE  ALT=\"B+=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=C=50 ALIGN=MIDDLE  ALT=\"A+=C=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "base <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=12cm ALIGN=MIDDLE  ALT=\"b=12cm\"   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=tan%2850+%29+=+h%2F%286cm%29 ALIGN=MIDDLE  ALT=\"tan%2850+%29+=+h%2F%286cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   (where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the altitude and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6cm ALIGN=MIDDLE  ALT=\"6cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > is half the base)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2850+%29+=+h%2F%286cm%29 ALIGN=MIDDLE  ALT=\"tan%2850+%29+=+h%2F%286cm%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=1.1918=+h%2F%286cm%29 ALIGN=MIDDLE  ALT=\"1.1918=+h%2F%286cm%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=1.1918%2A6cm=+h ALIGN=MIDDLE  ALT=\"1.1918%2A6cm=+h\"   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=7.15cm=+h ALIGN=MIDDLE  ALT=\"7.15cm=+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now we can find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > using Pythagorean theorem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=%28b%2F2%29%5E2%2Bh%5E2 ALIGN=MIDDLE  ALT=\"a%5E2=%28b%2F2%29%5E2%2Bh%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=a%5E2=%286cm%29%5E2%2B%287.15cm%29%5E2 ALIGN=MIDDLE  ALT=\"a%5E2=%286cm%29%5E2%2B%287.15cm%29%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=a%5E2=36cm%5E2%2B51cm%5E2 ALIGN=MIDDLE  ALT=\"a%5E2=36cm%5E2%2B51cm%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=a%5E2=87cm%5E2 ALIGN=MIDDLE  ALT=\"a%5E2=87cm%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=a=sqrt%2887cm%5E2%29 ALIGN=MIDDLE  ALT=\"a=sqrt%2887cm%5E2%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=a=9.33cm ALIGN=MIDDLE  ALT=\"a=9.33cm\"   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=P=2a%2Bb ALIGN=MIDDLE  ALT=\"P=2a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > (triangle is isosceles, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=c ALIGN=MIDDLE  ALT=\"a=c\"   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=P=2%2A9.33cm%2B12cm ALIGN=MIDDLE  ALT=\"P=2%2A9.33cm%2B12cm\"   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=P=18.66cm%2B12cm ALIGN=MIDDLE  ALT=\"P=18.66cm%2B12cm\"   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=P=30.66cm ALIGN=MIDDLE  ALT=\"P=30.66cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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