document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122325>Question 1122325</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two fire towers F and T are 30 km apart, F is due north of T. A fire at point G is observed from both towers. A watcher from F observes the bearing of the fire to be S 54°E and from T the bearing of the same fire is N 31°E. Find the distance of the fire from A.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #738419 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=738419\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this forms a triangle FGT.\r<BR>\n" );
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document.write( "angle GFT = 54 degrees.<BR>\n" );
document.write( "angle GTF = 31 degrees.\r<BR>\n" );
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document.write( "because the sum of the angle of a triangle is 180 degrees, then .....\r<BR>\n" );
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document.write( "angle FGT = 95 degrees.\r<BR>\n" );
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document.write( "the towers are 30 kilometers apart.\r<BR>\n" );
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document.write( "therefore FT = 30\r<BR>\n" );
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document.write( "use the law of sines to find the length of the other 2 sides of the triangle.\r<BR>\n" );
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document.write( "law of sines says that .....\r<BR>\n" );
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document.write( "a/sin(A) = b/sin(B) = c/sin(C)\r<BR>\n" );
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document.write( "this gets you FG / sin(31) = 30 / sin(95).\r<BR>\n" );
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document.write( "cross multiply to get FG * sin(95) = 30 * sin(31).\r<BR>\n" );
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document.write( "solve for FG to get FG = 30 * sin(31) / sin(95) = 15.5101631 kilometers.\r<BR>\n" );
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document.write( "this also gets you GT / sin(54) = 30 / sin(95).\r<BR>\n" );
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document.write( "cross multiply to get GT * sin(95) = 30 * sin(54).\r<BR>\n" );
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document.write( "solve for GT to get GT = 30 * sin(54) / sin(95) = 24.36321924 kilometers.\r<BR>\n" );
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document.write( "you want the distance of the fire from A?\r<BR>\n" );
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document.write( "there is no point A.\r<BR>\n" );
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document.write( "the fire is at point G.\r<BR>\n" );
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document.write( "the distance of the fire from point F is 15.5101631 kilometers.\r<BR>\n" );
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document.write( "the distance from point T is 24.36321924 kilometers.<BR>\n" );
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