document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=755371>Question 755371</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the missing side and angles of triangle ABC \r<BR>\n" );
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document.write( "sides: <BR>\n" );
document.write( "A= 12<BR>\n" );
document.write( "B= 13<BR>\n" );
document.write( "C= 17.69 \r<BR>\n" );
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document.write( "I had to find side C. So I took A^2 + B^2 = C^2 and put in 12^2 + 13^2 = C^2. 144+169=c^2. I added the left side and got 313 then I used the square root on both sides and got C = 17.69 \r<BR>\n" );
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document.write( "Angles: <BR>\n" );
document.write( "A= <BR>\n" );
document.write( "B=<BR>\n" );
document.write( "C= 76 degrees \r<BR>\n" );
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document.write( "How do I find the missing angles? Is my side C correct? Thank you for the help!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #459673 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=459673\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the missing side and angles of triangle ABC<BR>\n" );
document.write( "sides:<BR>\n" );
document.write( "A= 12<BR>\n" );
document.write( "B= 13<BR>\n" );
document.write( "C= 17.69<BR>\n" );
document.write( "I had to find side C. So I took A^2 + B^2 = C^2 and put in 12^2 + 13^2 = C^2. 144+169=c^2. I added the left side and got 313 then I used the square root on both sides and got C = 17.69<BR>\n" );
document.write( "Angles:<BR>\n" );
document.write( "A=<BR>\n" );
document.write( "B=<BR>\n" );
document.write( "C= 76 degrees<BR>\n" );
document.write( "How do I find the missing angles? Is my side C correct?<BR>\n" );
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document.write( "You have assumed this is a right triangle by using a^2 + b^2 = c^2<BR>\n" );
document.write( "But it's not, in a right triangle, the hypotenuse (c) is opposite<BR>\n" );
document.write( "the right angle (C) and here it is given as 76 degrees.<BR>\n" );
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document.write( "We have to use the law of cosines, which is:<BR>\n" );
document.write( " c^2 = a^2 + b^2 -2(ab)*cos(C), in this problem<BR>\n" );
document.write( "a=12, b=13, Angle C = 76; we will find side c:<BR>\n" );
document.write( "c^2 = 12^2 + 13^2 - 2(12*13)*cos(76)<BR>\n" );
document.write( "c^2 = 144 + 169 - 2(156)*.24192<BR>\n" );
document.write( "c^2 = 313-75.48<BR>\n" );
document.write( "c = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28237.52%29 ALIGN=MIDDLE  ALT=\"sqrt%28237.52%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c = 15.41 is side c<BR>\n" );
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document.write( "Use the law of sines to find Angle A<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Fsin%28A%29 ALIGN=MIDDLE  ALT=\"12%2Fsin%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.41%2Fsin%2876%29 ALIGN=MIDDLE  ALT=\"15.41%2Fsin%2876%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "15.41*sin(A) = 12*sin(76)<BR>\n" );
document.write( "sin(A) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11.6435%2F15.41 ALIGN=MIDDLE  ALT=\"11.6435%2F15.41\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "sin(A) .7556<BR>\n" );
document.write( "A = 49.1 degrees<BR>\n" );
document.write( "then<BR>\n" );
document.write( "B = 180 - 76 - 49.1<BR>\n" );
document.write( "B = 54.9 degrees<BR>\n" );
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document.write( "summarize<BR>\n" );
document.write( "sides<BR>\n" );
document.write( "a = 12<BR>\n" );
document.write( "b = 13<BR>\n" );
document.write( "c = 15.41<BR>\n" );
document.write( "Angles<BR>\n" );
document.write( "A = 49.1 degrees<BR>\n" );
document.write( "B = 54.9<BR>\n" );
document.write( "C = 76 degrees<BR>\n" );
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