document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180189>Question 1180189</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two​ fire-lookout stations are 29 miles ​apart, with station B directly east of station A. Both stations spot a fire. The bearing of the fire from station A is N35°E and the bearing of the fire from station B is N30°W. How​ far, to the nearest tenth of a​ mile, is the fire from each lookout​ station? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #809865 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=809865\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> two​ fire-lookout stations are 29 miles ​apart, with station B directly east of station A.<BR>\n" );
document.write( " Both stations spot a fire. <BR>\n" );
document.write( " The bearing of the fire from station A is N35°E and <BR>\n" );
document.write( " the bearing of the fire from station B is N30°W.<BR>\n" );
document.write( " How​ far, to the nearest tenth of a​ mile, is the fire from each lookout​ station?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Draw this out. Triangle ABC, where C is the point of the fire<BR>\n" );
document.write( "The line from A to B is horizontal to the the north-south lines so the interior angle of of the triangle:<BR>\n" );
document.write( "A = 90-35 = 55 degrees<BR>\n" );
document.write( "B = 90-30 = 60 degrees<BR>\n" );
document.write( "C = 180-55-60 = 65 degrees<BR>\n" );
document.write( ":<BR>\n" );
document.write( "label sides opposite the angles a, b, c<BR>\n" );
document.write( "Use the law of sine<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fsin%2855%29 ALIGN=MIDDLE  ALT=\"a%2Fsin%2855%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29%2Fsin%2865%29 ALIGN=MIDDLE  ALT=\"29%2Fsin%2865%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "sin(65)*a = 29 * sin(55)<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23.7554%2Fsin%2865%29 ALIGN=MIDDLE  ALT=\"23.7554%2Fsin%2865%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 26.2 mi from B to the fire<BR>\n" );
document.write( "and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fsin%2860%29 ALIGN=MIDDLE  ALT=\"b%2Fsin%2860%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29%2Fsin%2865%29 ALIGN=MIDDLE  ALT=\"29%2Fsin%2865%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "sin(65)*b = 29 * sin(60)<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25.1147%2Fsin%2865%29 ALIGN=MIDDLE  ALT=\"25.1147%2Fsin%2865%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = 27.7 mi from A to the fire\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );