document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=270967>Question 270967</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a plane is flying at 174 miles per hour with a heading of 50.5 degrees from due north. the wind is blowing a constant 23 miles per hour at 140.5 degrees from due north. find the ground speed and true course of the plane.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #198750 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=198750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Is the plane flying a heading of 50.5º?  If it's 50.5 \"from due north\", it could be 309.5º<BR>\n" );
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document.write( "Wind direction in aviation is the direction the wind is coming from.<BR>\n" );
document.write( "Is this wind from 140.5º?<BR>\n" );
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document.write( "The people writing textbooks should stick to subjects they know.  Headings are given to the whole degree, no 50.5 degs<BR>\n" );
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document.write( "I'll solve this, using that plane heading of 50.5, and the wind direction of 140.5 (coming from 140.5).<BR>\n" );
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document.write( "Notice they're 90º apart, so it's a right triangle with sides of 174 and 23.<BR>\n" );
document.write( "The resultang groundspeed is the hypotenuse:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5E2+=+174%5E2+%2B+23%5E2 ALIGN=MIDDLE  ALT=\"g%5E2+=+174%5E2+%2B+23%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "g = 175.5 mph<BR>\n" );
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document.write( "The angle between the plane's heading and it course is the arctan(23/174)<BR>\n" );
document.write( "=~ 7.53º<BR>\n" );
document.write( "If the wind direction uses from, that makes the ground track 43º<BR>\n" );
document.write( "If the wind direction uses to, it's 58º<BR>\n" );
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document.write( "PS miles per hour is not used in aviation, it's knots.<BR>\n" );
document.write( "It would be the \"wind is 140 at 20 knots\"\r<BR>\n" );
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