document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206227>Question 1206227</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An airplane starting from airport A,flies 300km east, then 350km 30°west of North, and then 150km north to arrive at airport B. Assuming that there was no wind on that day,<BR>\n" );
document.write( "a) determine in what direction should the pilot fly to travel directly from A to B?<BR>\n" );
document.write( "b) How far will the pilot fly to travel directly from A to B? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843522 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=843522\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> from point A, he goes east 300 kilometers.<BR>\n" );
document.write( "then he goes on a bearing of 30 degrees west of north for 350 kilometers.<BR>\n" );
document.write( "breaking this down to east/west and north/south directions, you get:<BR>\n" );
document.write( "west direction = 350 * sin(30) = east 175 kilometers.<BR>\n" );
document.write( "north direction = 350 * cos(30) = north 303.1088913 kilometers.<BR>\n" );
document.write( "then it's 150 kilometers in a north direction.\r<BR>\n" );
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document.write( "total east west direction = 300 kilometers east minus 175 kilometers west = 125 kilometers east.\r<BR>\n" );
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document.write( "total north south direction = 303.1088913 kilometers north plus 150 kilometers north = 453.1088913 kilometers north.\r<BR>\n" );
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document.write( "this forms a right triangle ABC where AC = 125 kilometers and BC = 453.1088913 kilometers.\r<BR>\n" );
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document.write( "the hypotenuse of this triangle is equal to AB which is equal to sqrt(125^2 + 453.1088913^2) = 470.0347512 kilometers.\r<BR>\n" );
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document.write( "that's the direct distance from A to B.\r<BR>\n" );
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document.write( "the direction of travel is arccos(125/470.0347512) = 74.5773165 degrees.<BR>\n" );
document.write( "90 minus that = 15.4226835 degrees.\r<BR>\n" );
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document.write( "point B is 15.4226835 degrees east of north from point A.\r<BR>\n" );
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document.write( "here's my diagram.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/022403.jpg\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
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