document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175814>Question 1175814</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man walks due west for 4 km he then change direction and walk on a bearing of 197° until he is southwest of his starting point how far is he then his starting point <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 #801510 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=801510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A bearing of 197 degrees is 17 degrees west of south.<br><BR>\n" );
document.write( "After walking 4 miles west from his starting point, his displacement in the x direction is 4 miles west and his displacement in the y direction is 0.<br><BR>\n" );
document.write( "In walking a distance d at an angle 17 degrees west of south, his displacement in the x direction is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Asin%2817%29 ALIGN=MIDDLE  ALT=\"d%2Asin%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (west), and his displacement in the y direction is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Acos%2817%29 ALIGN=MIDDLE  ALT=\"d%2Acos%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (south).<br><BR>\n" );
document.write( "So his total displacement is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Bd%2Asin%2817%29 ALIGN=MIDDLE  ALT=\"4%2Bd%2Asin%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > west and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Acos%2817%29 ALIGN=MIDDLE  ALT=\"d%2Acos%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > south.<br><BR>\n" );
document.write( "He is southwest of his starting point when his displacements west and south are equal.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Bd%2Asin%2817%29+=+d%2Acos%2817%29 ALIGN=MIDDLE  ALT=\"4%2Bd%2Asin%2817%29+=+d%2Acos%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That is not an equation you are going to solve manually; use a calculator.<br><BR>\n" );
document.write( "Then remember that the question asks for how far he is from his starting point.  The solution to the equation you solved is his displacement in each of the x and y directions; so his distance from his starting point is that displacement multiplied by the square root of 2.<br><BR>\n" );
document.write( "(To check your calculations, note my answer was a bit over 8km....)<br><BR>\n" );
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