document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121379>Question 1121379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two Coast Guard stations, A and B, are on an east-west line and are 72 km apart.   The bearing of a ship from station A is N 54o E, and the bearing of the same ship from station B is N 31o W.\r<BR>\n" );
document.write( "\n" );
document.write( "a)   How far is the ship from the east-west line connecting the two Coast Guard stations.<BR>\n" );
document.write( "b)   How far is the ship from station A?<BR>\n" );
document.write( "c)   How far is the ship from station B?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737251 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=737251\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the problem states it is giving bearings but really they are directions.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The direction to a point is stated as the number of degrees east or west of north or south.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The bearing to a point is the angle measured in a clockwise direction from the north line.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "I am using the information given as directions not bearings<BR>\n" );
document.write( ":\r<BR>\n" );
document.write( "\n" );
document.write( ":<BR>\n" );
document.write( "we need the internal angles of the triangle that joins the ship with stations A and B<BR>\n" );
document.write( ":<BR>\n" );
document.write( "90 degrees - 54 degrees = 36 degrees and 90 degrees - 31 = 59 degrees and the third angle at the ship is 180 - 36 -59 = 85 degrees<BR>\n" );
document.write( ":<BR>\n" );
document.write( "now use the law of sines<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a) sin(36) = distance from ship to AB / 61.9518  <BR>\n" );
document.write( ":<BR>\n" );
document.write( "distance from ship to AB = sin(36) * 61.9518 = 36.4144 km<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b) 72/sin(85) = distance from A to ship / sin(59)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "distance from A to ship = 72 * sin(59) / sin(85) = 61.9518 km<BR>\n" );
document.write( ":<BR>\n" );
document.write( "c) 72/sin(85) = distance from B to ship / sin(36)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "distance from B to ship = 72 * sin(36) / sin(85) = 42.4822 km<BR>\n" );
document.write( ":<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );