document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121144>Question 1121144</A>: <I><SPAN STYLE=\"word-break: break-all;\"> City C has a bearing of N 32o E from city A, and a bearing of N 22o W from city B.   City B is due east of city A, and is 24 miles from city C.   Find the area of triangle ABC.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737253 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=737253\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It helps to draw this<BR>\n" );
document.write( "ABC is the triangle.  a is 24 b is 32 and angle A is 58, angle B 68, and angle C 54<BR>\n" );
document.write( "From Law of Sines, 24/sin 58=b/sin 68=c/sin 54.<BR>\n" );
document.write( "24/sin 58=28.30<BR>\n" );
document.write( "b is 28.30 sin 68=26.24 <BR>\n" );
document.write( "c is 28.30 sin 54=22.90.  c is the base<BR>\n" );
document.write( "Can do the area from Hero's formula<BR>\n" );
document.write( "S=(1/2)(A+B+C)=(1/2)(24+26.24+22.90)=36.57<BR>\n" );
document.write( "S-A=12.57<BR>\n" );
document.write( "S-B=10.33<BR>\n" );
document.write( "S-C=13.67<BR>\n" );
document.write( "A=sqrt (S*(S-A)(S-B)(S-C))=sqrt (36.57*12.57*10.33*13.67)=254.78 mi^2  ANSWER\r<BR>\n" );
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document.write( "Can check with side c=22.90, so altitude must be 509.56/22.90, or 22.25 mi\r<BR>\n" );
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document.write( "with one triangle, 26.24=alt/sin 58=22.25 mi<BR>\n" );
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