document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=288384>Question 288384</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't understand how to solve these two question. Can someone please explain in detail?\r<BR>\n" );
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document.write( "1. A ranger in fire tower A spots a fire at a direction of 40 degrees. A ranger in fire tower B, which is 28 miles away directly east of tower A, spots the same fire at a direction of 330 degrees. How far from tower A is the fire?\r<BR>\n" );
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document.write( "2. A boat leaves the dock and sails in a direction of 70 degrees. Once reaching its destination on the opposite shore, it sails in a direction of 272 degrees and docks 150 km north of its original starting position. What is the total distance the boat has traveled?\r<BR>\n" );
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document.write( "I appreciate your help.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #209032 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=209032\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. A ranger in fire tower A spots a fire at a direction of 40 degrees. A ranger in fire tower B, which is 28 miles away directly east of tower A, spots the same fire at a direction of 330 degrees. How far from tower A is the fire?<BR>\n" );
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document.write( "Directions are given using North as 0/360º<BR>\n" );
document.write( "Points A, B and the fire (point F) form a triangle.  Side AB is 28 miles<BR>\n" );
document.write( "Angle A is 90 - 40 = 50º<BR>\n" );
document.write( "Angle B is 60º (330-270)<BR>\n" );
document.write( "Angle F is 70º (180 - 50 - 60)<BR>\n" );
document.write( "Use the law of sines to find AF<BR>\n" );
document.write( "AF/sin(60) = 28/sin(70)<BR>\n" );
document.write( "AF =~ 25.805 miles<BR>\n" );
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document.write( "2. A boat leaves the dock and sails in a direction of 70 degrees. Once reaching its destination on the opposite shore, it sails in a direction of 272 degrees and docks 150 km north of its original starting position. What is the total distance the boat has traveled? <BR>\n" );
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document.write( "S = starting point<BR>\n" );
document.write( "D = destination<BR>\n" );
document.write( "N = point 150 km north of S<BR>\n" );
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document.write( "Side SN = 150 km<BR>\n" );
document.write( "Angle S = 70º<BR>\n" );
document.write( "Angle D = 22º<BR>\n" );
document.write( "Angle N = 88º<BR>\n" );
document.write( "Use the Sine Law as above.<BR>\n" );
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document.write( "Getting the angles from the given directions isn't familiar to most people.<BR>\n" );
document.write( "Email me and I'll send sketches showing how it's done.<BR>\n" );
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