document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1079182>Question 1079182</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, please help me solve this question below.\r<BR>\n" );
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document.write( "the interior angles of a triangle are 115,20, and 45. The longest side is 13 am longer then the shortest side. determine the perimeter of the triangle to the nearest cm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #693525 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=693525\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The numbers given for the interior angles of the triangle must be their measures in degrees.<BR>\n" );
document.write( "They add to 180, as they should, and giving just two of them would be enough information.<BR>\n" );
document.write( "Let it be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= length of the shortest side, in cm<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= length of the medium length side, in cm<BR>\n" );
document.write( "we know that in a triangle<BR>\n" );
document.write( "shorter side is opposite smaller angle,<BR>\n" );
document.write( "so the triangle looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C100%2C-17%2C7%2C-1.5%2C6.5%2C%0D%0Atriangle%28-15.31%2C0%2C5.57%2C0%2C0%2C5.57%29%2C%0D%0Aarc%285.57%2C0%2C7%2C7%2C180%2C225%29%2Clocate%282.4%2C1.8%2C45%5Eo%29%2C%0D%0Aarc%28-15.31%2C0%2C7%2C7%2C-20%2C0%29%2Clocate%28-11.7%2C1.8%2C20%5Eo%29%2C%0D%0Aarc%280%2C5.57%2C4%2C4%2C45%2C160%29%2Clocate%28-3%2C5%2C115%5Eo%29%2C%0D%0Alocate%28-6%2C0%2Cx%2B13cm%29%2Clocate%282.8%2C3.8%2Cx%29%2C%0D%0Alocate%28-7.3%2C4.4%2Cy%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Law of sines agrees that shorter side is opposite smaller angle,<BR>\n" );
document.write( "but goes further and says that<BR>\n" );
document.write( "the ratio of side length to sine of opposite angle is the same for all sides.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fsin%2820%5Eo%29=%28x%2B13%29%2Fsin%28115%5Eo%29=y%2Fsin%2845%5Eo%29 ALIGN=MIDDLE  ALT=\"x%2Fsin%2820%5Eo%29=%28x%2B13%29%2Fsin%28115%5Eo%29=y%2Fsin%2845%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we can find the approximate values of those sines.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2820%5Eo%29=0.34202 ALIGN=MIDDLE  ALT=\"sin%2820%5Eo%29=0.34202\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28115%5Eo%29=0.90631 ALIGN=MIDDLE  ALT=\"sin%28115%5Eo%29=0.90631\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2845%5Eo%29=0.70711 ALIGN=MIDDLE  ALT=\"sin%2845%5Eo%29=0.70711\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We can solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fsin%2820%5Eo%29=%28x%2B13%29%2Fsin%28115%5Eo%29 ALIGN=MIDDLE  ALT=\"x%2Fsin%2820%5Eo%29=%28x%2B13%29%2Fsin%28115%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fsin%2820%5Eo%29=%28x%2B13%29%2Fsin%28115%5Eo%29 ALIGN=MIDDLE  ALT=\"x%2Fsin%2820%5Eo%29=%28x%2B13%29%2Fsin%28115%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F0.34202=%28x%2B13%29%2F0.90631 ALIGN=MIDDLE  ALT=\"x%2F0.34202=%28x%2B13%29%2F0.90631\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.90631x=0.34202%28x%2B13%29 ALIGN=MIDDLE  ALT=\"0.90631x=0.34202%28x%2B13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.90631x=0.34202x%2B0.34202%2A13 ALIGN=MIDDLE  ALT=\"0.90631x=0.34202x%2B0.34202%2A13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.90631x-0.34202x=0.34202%2A13 ALIGN=MIDDLE  ALT=\"0.90631x-0.34202x=0.34202%2A13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.90631-0.34202%29x=0.34202%2A13 ALIGN=MIDDLE  ALT=\"%280.90631-0.34202%29x=0.34202%2A13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.56429x=0.34202%2A13 ALIGN=MIDDLE  ALT=\"0.56429x=0.34202%2A13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.56429x=4.44626 ALIGN=MIDDLE  ALT=\"0.56429x=4.44626\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4.44626%2F0.56429 ALIGN=MIDDLE  ALT=\"x=4.44626%2F0.56429\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=approximately+7.88 ALIGN=MIDDLE  ALT=\"x=approximately+7.88\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B13=approximately ALIGN=MIDDLE  ALT=\"x%2B13=approximately\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.88%2B13=20.88 ALIGN=MIDDLE  ALT=\"7.88%2B13=20.88\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fsin%2820%5Eo%29=y%2Fsin%2845%5Eo%29 ALIGN=MIDDLE  ALT=\"x%2Fsin%2820%5Eo%29=y%2Fsin%2845%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fsin%2820%5Eo%29=y%2Fsin%2845%5Eo%29 ALIGN=MIDDLE  ALT=\"x%2Fsin%2820%5Eo%29=y%2Fsin%2845%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F0.34202=y%2F0.70711 ALIGN=MIDDLE  ALT=\"x%2F0.34202=y%2F0.70711\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.56429x=0.34202%2A13 ALIGN=MIDDLE  ALT=\"0.56429x=0.34202%2A13\"   DISABLED_style= \"max-width:90%; height:auto;\" > (above), we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F0.34202=13%2F0.56429 ALIGN=MIDDLE  ALT=\"x%2F0.34202=13%2F0.56429\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so we can use that rather than the already rounded <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=approximately+7.88 ALIGN=MIDDLE  ALT=\"x=approximately+7.88\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F0.70711=13%2F0.56429 ALIGN=MIDDLE  ALT=\"y%2F0.70711=13%2F0.56429\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=13%2A0.70711%2F0.56429 ALIGN=MIDDLE  ALT=\"y=13%2A0.70711%2F0.56429\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=approximately+16.29 ALIGN=MIDDLE  ALT=\"y=approximately+16.29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "S]Now, knowing the lengths of all 3 sides to 2 decimal places,<BR>\n" );
document.write( "we add them to find the approximate perimeter,<BR>\n" );
document.write( "to be reported further rounded as a whole number.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20.88cm%2B16.29cm%2B5.88cm=45.05cm ALIGN=MIDDLE  ALT=\"20.88cm%2B16.29cm%2B5.88cm=45.05cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To the nearest cm, the perimeter is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2845cm%29 ALIGN=MIDDLE  ALT=\"highlight%2845cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );