document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112902>Question 1112902</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ranger in tower A spots a fire at a direction of 352 degrees. A ranger in tower&#8203; B, located 45 mi at a direction of 41 degrees from tower&#8203; A, spots the fire at a direction of 294 degrees. How far from tower A is the&#8203; fire? How far from tower&#8203; B? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #727928 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=727928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=solver91311&illustration_name=FireObservers\">\r<BR>\n" );
document.write( "\n" );
document.write( "Direction angles (typically) are measured clockwise from North, which is typically in the direction of the positive <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-axis on a coordinate plane.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thus, if the direction of the fire from A is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 352^{\circ}\">, then the angle measured on the coordinate plane must be 360 - 352 + 90, that is *<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 98^{\circ}\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The direction of B from A is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 41^{\circ}\">, so measured on the coordinate plane the angle is 90 - 41 = 49.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That means that the angle from the line between A and B to the line between A and the Fire must be 98 - 49 = 49 degrees.  Now we have angle A.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Considering a line parallel to the x-axis through point B, measured in the coordinate plane would be 360 - 294 + 90 = 156.  Continuing clockwise, the angle from the line between B and the Fire and the horizonal line through B is 180 - 156 = 24.  By opposite interior angles of a transversal of two parallel lines, the angle from the line between A and B and the horizontal line through B is 49 degrees.  Hence, the angle from the line between A and B and the line between B and the Fire is 24 + 49 = 73 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then the final angle of the triangle, at the point of the fire is 180 - (73 + 49) = 66 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the Law of Sines:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{45}{\sin(66)}\ =\ \frac{\overline{AF}}{\sin(73)}\ =\ \frac{\overline{BF}}{\sin(49)}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The rest is just calculator work.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );