document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106077>Question 1106077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Find the angle with the smallest measure in triangle VUW. \r<BR>\n" );
document.write( "\n" );
document.write( "2. Find the angle with the largest measure in UWX. \r<BR>\n" );
document.write( "\n" );
document.write( "Here's the picture of the angles for the question I'm trying to solve for: \r<BR>\n" );
document.write( "\n" );
document.write( "http://image.ibb.co/cmkkbm/5_5b.png\r<BR>\n" );
document.write( "\n" );
document.write( "Any help is appreciated.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721041 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5347)</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=721041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem seems designed as an example of law of cosines.<BR>\n" );
document.write( "Right triangles are easier to solve, but if you cannot find a right angle,<BR>\n" );
document.write( "your tools are law of sines and law of cosines.<BR>\n" );
document.write( "Law of sines applies easily when you have the measures of an angle and the opposite side. If you only have 3 sides, you use law of cosines.<BR>\n" );
document.write( "Law of cosines is given as a formula like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=b%5E2%2Bc%5E2-2%2Ab%2Ac%2Acos%28A%29 ALIGN=MIDDLE  ALT=\"a%5E2=b%5E2%2Bc%5E2-2%2Ab%2Ac%2Acos%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > that turns into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=b%5E2%2Bc%5E2 ALIGN=MIDDLE  ALT=\"a%5E2=b%5E2%2Bc%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=90%5Eo ALIGN=MIDDLE  ALT=\"A=90%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "With that formula and the lengths of 3 sides, you call the angle you are looking for angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for A.<BR>\n" );
document.write( "If you are supposed to write the formula, write it like the instructor or the book prefers it.<BR>\n" );
document.write( "It could be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2%2Bb%5E2-2%2Aa%2Ab%2Acos%28C%29 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2%2Bb%5E2-2%2Aa%2Ab%2Acos%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and you would be looking for angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1. Triangle VUW has side lengths <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The shorter side, with length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is opposite vertex U,<BR>\n" );
document.write( "so angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U ALIGN=MIDDLE  ALT=\"U\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the smallest angle,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the side length that is squared on one the left side of the equal sign in the law of cosines formula.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2=9%5E2%2B9%5E2-2%2A9%2A9%2Acos%28U%29 ALIGN=MIDDLE  ALT=\"5%5E2=9%5E2%2B9%5E2-2%2A9%2A9%2Acos%28U%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=81%2B81-162cos%28U%29 ALIGN=MIDDLE  ALT=\"25=81%2B81-162cos%28U%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=162-162cos%28U%29 ALIGN=MIDDLE  ALT=\"25=162-162cos%28U%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-137=-162cos%28U%29 ALIGN=MIDDLE  ALT=\"-137=-162cos%28U%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%28U%29=137%2F162 ALIGN=MIDDLE  ALT=\"cos%28U%29=137%2F162\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28U%29=0.84568 ALIGN=MIDDLE  ALT=\"cos%28U%29=0.84568\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U=32.26%5Eo ALIGN=MIDDLE  ALT=\"U=32.26%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded)<BR>\n" );
document.write( " <BR>\n" );
document.write( "2. The side lengths of triangle UWX are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The longer side, with length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is opposite vertex X,<BR>\n" );
document.write( "so angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the largest angle,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the side length that is squared on one the left side of the equal sign in the law of cosines formula.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E2=8%5E2%2B7%5E2-2%2A8%2A7%2Acos%28X%29 ALIGN=MIDDLE  ALT=\"9%5E2=8%5E2%2B7%5E2-2%2A8%2A7%2Acos%28X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81=64%2B49-112cos%28X%29 ALIGN=MIDDLE  ALT=\"81=64%2B49-112cos%28X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81-113-112cos%28X%29 ALIGN=MIDDLE  ALT=\"81-113-112cos%28X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32=-112cos%28X%29 ALIGN=MIDDLE  ALT=\"-32=-112cos%28X%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%28X%29=32%2F112 ALIGN=MIDDLE  ALT=\"cos%28X%29=32%2F112\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28X%29=0.2857 ALIGN=MIDDLE  ALT=\"cos%28X%29=0.2857\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=73.40%5Eo ALIGN=MIDDLE  ALT=\"X=73.40%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );