document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=868331>Question 868331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The side of the triangle are 20m, 25m , and 30m repectively. Find the Length of the altitude to the  longest side? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #523531 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=523531\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use Law of Cosines...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A picture will help but is <b>not</b> here included.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Pick the interior angle at the vertex of the 20 m and 30 m sides. Call the angle measure, t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5E2%2B30%5E2-2%2A20%2A30%2Acos%28t%29=25%5E2 ALIGN=MIDDLE  ALT=\"20%5E2%2B30%5E2-2%2A20%2A30%2Acos%28t%29=25%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1300-625=1200cos%28t%29 ALIGN=MIDDLE  ALT=\"1300-625=1200cos%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28t%29=675%2F1200 ALIGN=MIDDLE  ALT=\"cos%28t%29=675%2F1200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28t%29=9%2F16 ALIGN=MIDDLE  ALT=\"cos%28t%29=9%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "What is this value of t?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=arcos%289%2F16%29=55.7711 ALIGN=MIDDLE  ALT=\"arcos%289%2F16%29=55.7711\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees for more accuracy than needed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the 20 meter length side as the hypotenuse of a right triangle which contains the altitude and part of the base side; we do not need the base side nor part of it here.  We only want to compute the altitude.  This altitude is:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%2820%2Asin%2855.7711%29%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%2820%2Asin%2855.7711%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "16.5 meters. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );