document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=617680>Question 617680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the legnth of the hypotenuse of a 30-60-90 triangle whose longer leg has a length of 6 radical 3 ft?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #388545 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=388545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SHORT ANSWER:<BR>\n" );
document.write( "The fastest way to write an answer seems to be invoking trigonometric ratios.<BR>\n" );
document.write( "The long leg is opposite the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%5Eo ALIGN=MIDDLE  ALT=\"60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > angle, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2860%5Eo%29=long_leg%2Fhypotenuse ALIGN=MIDDLE  ALT=\"sin%2860%5Eo%29=long_leg%2Fhypotenuse\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hypotenuse=sin%2860%5Eo%29%2Along_leg ALIGN=MIDDLE  ALT=\"hypotenuse=sin%2860%5Eo%29%2Along_leg\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "long_leg=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2860%5Eo%29=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sin%2860%5Eo%29=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Putting it al together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hypotenuse=%28sqrt%283%29%2F2%29%286%2Asqrt%283%29%29=3%2Asqrt%283%29%2Asqrt%283%29=3%2A3=highlight%289%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "HOW WE KNOW THOSE TRIGONOMETRIC RATIOS:<BR>\n" );
document.write( "A 30-60-90 triangle is half of an equilateral triangle:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C10%2C-6%2C6%2C%0D%0Atriangle%280%2C5%2C0%2C-5%2C8.66%2C0%29%2C%0D%0Arectangle%280%2C0%2C0.3%2C0.3%29%2C%0D%0Ared%28line%280%2C0%2C8.66%2C0%29%29%2C%0D%0Alocate%28-.5%2C0.3%2CA%29%2C+locate%28-0.5%2C5.5%2CB%29%2C%0D%0Alocate%28-.5%2C-5%2CD%29%2Clocate%288.7%2C0.3%2CC%29%2C%0D%0Alocate%284.5%2C3%2Ca%29%2Clocate%280.1%2C2.8%2Cc%29%2Clocate%284%2C0.6%2Cb%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=AD ALIGN=MIDDLE  ALT=\"AB=AD\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=BC=AD=2%2AAB=2c ALIGN=MIDDLE  ALT=\"a=BC=AD=2%2AAB=2c\"   DISABLED_style= \"max-width:90%; height:auto;\" > (The hypotenuse is twice as long as the short leg).<BR>\n" );
document.write( "Using the Pythagorean theorem (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2Bc%5E2=a%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2Bc%5E2=a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2Bc%5E2=%282c%29%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2Bc%5E2=%282c%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2Bc%5E2=4c%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2Bc%5E2=4c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=4c%5E2-c%5E2 ALIGN=MIDDLE  ALT=\"b%5E2=4c%5E2-c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=3c%5E2 ALIGN=MIDDLE  ALT=\"b%5E2=3c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=sqrt%283c%5E2%29 ALIGN=MIDDLE  ALT=\"b=sqrt%283c%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=sqrt%283%29%2Ac ALIGN=MIDDLE  ALT=\"b=sqrt%283%29%2Ac\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the trigonometric ratios in a 30-60-90 triangle are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2830%5Eo%29=cos%2860%5Eo%29=c%2Fa=c%2F%282c%29=1%2F2 ALIGN=MIDDLE  ALT=\"sin%2830%5Eo%29=cos%2860%5Eo%29=c%2Fa=c%2F%282c%29=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=cos%2830%5Eo%29=sin%2860%5Eo%29=b%2Fa=%28sqrt%283%29%2Ac%29%2F%282%2Ac%29=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"cos%2830%5Eo%29=sin%2860%5Eo%29=b%2Fa=%28sqrt%283%29%2Ac%29%2F%282%2Ac%29=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2830%5Eo%29=cot%2860%5Eo%29=c%2Fb=c%2F%28sqrt%283%29%2Ac%29=1%2Fsqrt%283%29=sqrt%283%29%2F3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%2830%5Eo%29=+tan%2860%5Eo%29=b%2Fc=sqrt%283%29%2Ac%2Fc=sqrt%283%29 ALIGN=MIDDLE  ALT=\"cot%2830%5Eo%29=+tan%2860%5Eo%29=b%2Fc=sqrt%283%29%2Ac%2Fc=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );