document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=858520>Question 858520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a 30 60 90 triangle and in my class we are learning about the sides and the radicals. So in this problem the longer leg is 12. and we don't know what the short leg or the hypotenuse is. But that is what we want to know. All I know is 12 = x rad3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #517240 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=517240\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the angles are 30-60-90 and the sides opposite <BR>\n" );
document.write( "these angles are a, b, and c, then you know that<BR>\n" );
document.write( "the sides are in these proportions:<BR>\n" );
document.write( "a : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+ ALIGN=MIDDLE  ALT=\"+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%283%29+ ALIGN=MIDDLE  ALT=\"+sqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+ ALIGN=MIDDLE  ALT=\"+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "This checks out because:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%5E2+%2B+%28+sqrt%283%29+%29%5E2+=+2%5E2+ ALIGN=MIDDLE  ALT=\"+1%5E2+%2B+%28+sqrt%283%29+%29%5E2+=+2%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+%2B+3+=+4+ ALIGN=MIDDLE  ALT=\"+1+%2B+3+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Once you put a value on one leg, the <BR>\n" );
document.write( "other legs are known:<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+12+ ALIGN=MIDDLE  ALT=\"+b+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( longer leg )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2Fb+=+1%2F%28sqrt%283%29+%29+ ALIGN=MIDDLE  ALT=\"+a%2Fb+=+1%2F%28sqrt%283%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=+a%2F12+=+1%2F%28sqrt%283%29+%29+ ALIGN=MIDDLE  ALT=\"+a%2F12+=+1%2F%28sqrt%283%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12%2Asqrt%283%29+ ALIGN=MIDDLE  ALT=\"+12%2Asqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2Asqrt%283%29+=+12+ ALIGN=MIDDLE  ALT=\"+a%2Asqrt%283%29+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+12%2Fsqrt%283%29+ ALIGN=MIDDLE  ALT=\"+a+=+12%2Fsqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "That's the answer. You can check by <BR>\n" );
document.write( "finding c<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++a%2Fc+=+1%2F2+ ALIGN=MIDDLE  ALT=\"++a%2Fc+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F2+=+%28+12%2Fsqrt%283%29+%29+%2F+c+ ALIGN=MIDDLE  ALT=\"+1%2F2+=+%28+12%2Fsqrt%283%29+%29+%2F+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+24%2Fsqrt%283%29+ ALIGN=MIDDLE  ALT=\"+c+=+24%2Fsqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5E2+%2B+b%5E2+=+c%5E2+ ALIGN=MIDDLE  ALT=\"+a%5E2+%2B+b%5E2+=+c%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+12%2Fsqrt%283%29+%29%5E2+%2B+12%5E2+=+%28+24%2Fsqrt%283%29+%29%5E2+ ALIGN=MIDDLE  ALT=\"+%28+12%2Fsqrt%283%29+%29%5E2+%2B+12%5E2+=+%28+24%2Fsqrt%283%29+%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+144%2F3+%2B+144+=+576%2F3+ ALIGN=MIDDLE  ALT=\"+144%2F3+%2B+144+=+576%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+144+%2B+3%2A144+=+576+ ALIGN=MIDDLE  ALT=\"+144+%2B+3%2A144+=+576+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+144+%2B+432+=+576+ ALIGN=MIDDLE  ALT=\"+144+%2B+432+=+576+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+576+=+576+ ALIGN=MIDDLE  ALT=\"+576+=+576+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );