document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=488945>Question 488945</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this question: Villages A,B,C and D are such that B is 4km due east of A, C is 3km due south of B and D is 4km South50degreeWest from C. Calculate the distance and bearing of A from D. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333902 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=333902\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this question: Villages A,B,C and D are such that B is 4km due east of A, C is 3km due south of B and D is 4km South50degreeWest from C. Calculate the distance and bearing of A from D.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "For you to understand my solution, we must work from the same diagram, so let us try to draw one:\r<BR>\n" );
document.write( "\n" );
document.write( "Starting from point A, draw a 4 km horizontal line to B. (B is due East of A)<BR>\n" );
document.write( "From B, draw a 3 km vertical down to C. (C is due South of B)<BR>\n" );
document.write( "From C, draw a 4 km line rotated 50º clockwise from vertical to D. (D is 50º west of south from C)<BR>\n" );
document.write( "Draw a line from D back to A.<BR>\n" );
document.write( ".. <BR>\n" );
document.write( "This is the basic diagram, but we need to construct additional lines and points:<BR>\n" );
document.write( "From D, draw a vertical line up until is intersects with line AB. Call this point E.<BR>\n" );
document.write( "Also from D, draw horizontal line (right) that intersects with a vertical line drawn from C. Call this point F.<BR>\n" );
document.write( "Also from D, draw horizontal line(left) that intersects with a vertical line drawn from A. Call this point G.<BR>\n" );
document.write( "We now should have a rectangle with the four corners labeled ABFG.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "DF/4=sin 50º<BR>\n" );
document.write( "DF=4Sin50º=3.06<BR>\n" );
document.write( "..<BR>\n" );
document.write( "CF/4=Cos 50º<BR>\n" );
document.write( "CF=4cos50º=2.57<BR>\n" );
document.write( "..<BR>\n" );
document.write( "AE=4-DF=4-3.06=.94<BR>\n" );
document.write( "ED=3+CF=3+2.57=5.57<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Bearing angle=angle ADE; call this angle x<BR>\n" );
document.write( "tan x=AE/ED=.94/5.57=.1688<BR>\n" );
document.write( "arctan(.1688)=9.58º<BR>\n" );
document.write( "x=9.58º<BR>\n" );
document.write( "AD=AE/sinx=.94/sin 9.58º=5.64 km<BR>\n" );
document.write( "Ans:<BR>\n" );
document.write( "Bearing of A from D is 5.64 km N9.58ºW<BR>\n" );
document.write( "..<BR>\n" );
document.write( "I hope this came out ok.\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );