document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=508239>Question 508239</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Airport B is 300 mi from airport A at a bearing N 50°E (see the figure). A pilot wishing to fly from A to B mistakenly flies due east at 175 mi/h for 35 minutes, when he notices his error\r<BR>\n" );
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document.write( "How far is the pilot from his destination at the time he notices the error? Give your answer correct to the nearest mile?\r<BR>\n" );
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document.write( "What bearing should he head his plane in order to arrive at airport B? Give your answer correct to the nearest degree? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #341080 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=341080\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Airport B is 300 mi from airport A at a bearing N 50°E (see the figure). A pilot wishing to fly from A to B mistakenly flies due east at 175 mi/h for 35 minutes, when he notices his error <BR>\n" );
document.write( "How far is the pilot from his destination at the time he notices the error? Give your answer correct to the nearest mile? <BR>\n" );
document.write( "What bearing should he head his plane in order to arrive at airport B? Give your answer correct to the nearest degree?<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Draw a line from point A to point B. This line is 300 mi long and makes an angle of 40º from the horizontal (based on N50ºE bearing). From point A draw a horizontal line to point C. This line=(35/60)*175=102.1 mi. Draw a line connecting point C to point B. You now have a triangle with sides AB=300 mi and AC=102.1 mi and their included angle of 40º.<BR>\n" );
document.write( "Using Law of cosines to find CB:<BR>\n" );
document.write( "(CB)^2=(AB)^2+(AC)^2-2*AB*AC*cos 40º<BR>\n" );
document.write( "(CB)^2=(300)^2+(102.1)^2-2*300*102.1*cos 40º<BR>\n" );
document.write( "(CB)^2=90000+10424-46928=53497<BR>\n" );
document.write( "CB=&#8730;53497=231 mi<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Solving for bearing<BR>\n" );
document.write( "CB/sin 40º=300/sin(ACB)<BR>\n" );
document.write( "231/sin40º=300/sin(ACB)<BR>\n" );
document.write( "sin(ACB)=(300/231)sin40º<BR>\n" );
document.write( "sin(ACB)=.8348<BR>\n" );
document.write( "ACB=123.4º<BR>\n" );
document.write( "new heading=90-123.4=33.4º<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "The pilot is 231 mi from his destination at the time he notices the error.<BR>\n" );
document.write( "In order to arrive at airport B, the new heading should be N33.4ºW </SPAN>\n" );
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