document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189695>Question 1189695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> iven right △ABC \r<BR>\n" );
document.write( "\n" );
document.write( "m∠N = <BR>\n" );
document.write( " <BR>\n" );
document.write( "                   o= 5.7\r<BR>\n" );
document.write( "\n" );
document.write( "m∠M = <BR>\n" );
document.write( " <BR>\n" );
document.write( "                   n= 5\r<BR>\n" );
document.write( "\n" );
document.write( "m∠O = 90°                    m=<BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821141 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=821141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'm not sure why you mentioned triangle ABC, but I'll ignore that portion. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Drawing:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/Gtq9Kdb.png\"><BR>\n" );
document.write( "The diagram isn't to scale\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the pythagorean theorem to find the missing side m<BR>\n" );
document.write( "m^2 + n^2 = o^2<BR>\n" );
document.write( "m^2 + 5^2 = (5.7)^2<BR>\n" );
document.write( "m^2 + 25 = 32.49<BR>\n" );
document.write( "m^2 = 32.49 - 25<BR>\n" );
document.write( "m^2 = 7.49<BR>\n" );
document.write( "m = sqrt(7.49)<BR>\n" );
document.write( "m = 2.736786<BR>\n" );
document.write( "That value is approximate\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now use the tangent ratio to help find angle M<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(M) = m/n<BR>\n" );
document.write( "tan(M) = 2.736786/5<BR>\n" );
document.write( "M = arctan(2.736786/5)<BR>\n" );
document.write( "M = 28.6944097<BR>\n" );
document.write( "That value is approximate\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Do the same idea for angle N<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(N) = n/m<BR>\n" );
document.write( "tan(N) = 5/2.736786<BR>\n" );
document.write( "N = arctan(5/2.736786)<BR>\n" );
document.write( "N = 61.3055903<BR>\n" );
document.write( "That value is approximate\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Or notice that<BR>\n" );
document.write( "M+N = 90<BR>\n" );
document.write( "N = 90-M<BR>\n" );
document.write( "N = 90-28.6944097<BR>\n" );
document.write( "N = 61.3055903\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=============================================\r<BR>\n" );
document.write( "\n" );
document.write( "Summary:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Side lengths:<BR>\n" );
document.write( "<font color=red>m = 2.736786</font> (approximate)<BR>\n" );
document.write( "<font color=black>n = 5</font> <BR>\n" );
document.write( "<font color=black>o = 5.7</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Angles<BR>\n" );
document.write( "<font color=red>M = 28.6944097 degrees</font> (approximate)<BR>\n" );
document.write( "<font color=red>N = 61.3055903 degrees</font> (approximate)<BR>\n" );
document.write( "<font color=black>O = 90 degrees</font><BR>\n" );
document.write( "</font><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );