document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=703753>Question 703753</A>: <I><SPAN STYLE=\"word-break: break-all;\"> suppose that the end points of the longer leg of a 30-60-90 triangle are (-3,5) and (2-1). what is the length of the shorter leg? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #433815 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=433815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The difference in x-coordinates between point (-3,5) and point(2,-1) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-%28-3%29=2%2B3=5 ALIGN=MIDDLE  ALT=\"2-%28-3%29=2%2B3=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The difference in y-coordinates between point (-3,5) and point(2,-1) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-%28-1%29=5%2B1=6 ALIGN=MIDDLE  ALT=\"5-%28-1%29=5%2B1=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The length of the longer leg connection those two points is<BR>\n" );
document.write( "longer leg = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%5E2%2B6%5E2%29=sqrt%2825%2B36%29=sqrt%2861%29 ALIGN=MIDDLE  ALT=\"sqrt%285%5E2%2B6%5E2%29=sqrt%2825%2B36%29=sqrt%2861%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That is not a friendly number.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Had the second point been (1,-2), the length would have been much friendlier:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281-%28-3%29%29%5E2%2B%285-2%29%5E2%29=sqrt%284%5E2%2B3%5E2%29=sqrt%2816%2B9%29=sqrt%2825%29=5 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "In a 30-60-90 triangle the shorter leg is opposite the smaller, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5Eo ALIGN=MIDDLE  ALT=\"30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > angle, and the longer leg is adjacent to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5Eo ALIGN=MIDDLE  ALT=\"30%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=tan%2830%5Eo%29=sqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"tan%2830%5Eo%29=sqrt%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=(shorter leg)/(longer leg) --> shorter leg =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2F3%29 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >(longer leg)<BR>\n" );
document.write( " <BR>\n" );
document.write( "So, if longer leg = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2861%29 ALIGN=MIDDLE  ALT=\"sqrt%2861%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Shorter leg = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2F3%29sqrt%2861%29=sqrt%283%2A61%29%2F3=sqrt%28183%29%2F3 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2F3%29sqrt%2861%29=sqrt%283%2A61%29%2F3=sqrt%28183%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >= about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.5 ALIGN=MIDDLE  ALT=\"4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The drawing below shows one of the four possible such triangles (with the vertices circled):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C360%2C-5%2C5%2C-6%2C6%2C%0D%0Agrid%281%29%2C%0D%0Ared%28circle%28-3%2C5%2C0.2%29%29%2Cred%28circle%282%2C-1%2C0.2%29%29%2Ccircle%28-1.464%2C-3.887%2C0.2%29%2C%0D%0Ablue%28triangle%28-3%2C5%2C2%2C-1%2C-1.464%2C-3.887%29%29%2C%0D%0Agreen%28circle%282%2C-1%2C4.5%29%29%2Clocate%282.2%2C-1%2C%22%282%2C-1%29%22%29%2Clocate%28-2.8%2C5%2C%22%28-3%2C5%29%22%29%2C%0D%0Agreen%28line%28-4%2C-6%2C-1.464%2C-3.887%29%29%2Cgreen%28line%282%2C-1%2C8%2C4%29%29%2C%0D%0Agreen%28line%28-3%2C5%2C-8%2C11%29%29%2Cgreen%28line%282%2C-1%2C7%2C-7%29%29%2C%0D%0Agreen%28line%28-9%2C0%2C3%2C10%29%29%2Cred%28line%282%2C-1%2C-3%2C5%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > All 4 have the red leg and a short leg on a perpendicular green line, but they could be flipped. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );