document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=583736>Question 583736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An airplane with a speed of 160 knots is headed east while a 24-knot wind is blowing from 240. Find the course and round 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 #372569 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=372569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An airplane with a speed of 160 knots is headed east while a 24-knot wind is blowing from 240. Find the course and round to the nearest degree.<BR>\n" );
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document.write( "The vectors make a triangle with 160 on the base, a 150 deg angle and the 24 side.  If you plot it on the x-y plane with the plane's speed from (0,0) to (160,0) and the wind vector starting at (160,0) length 24, the internal angle is 150 degs.<BR>\n" );
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document.write( "find the 3rd side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+sqrt%28160%5E2+%2B+24%5E2+-+2%2A160%2A24%2Acos%28150%29%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%28160%5E2+%2B+24%5E2+-+2%2A160%2A24%2Acos%28150%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "r =~ 181.18 knots (the plane's groundspeed)<BR>\n" );
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document.write( "Use the Sine Law to find the angle at the origin:<BR>\n" );
document.write( "181.18/sin(150) = 24/sin(A)<BR>\n" );
document.write( "sin(A) = 24*sin(150)/181.18<BR>\n" );
document.write( "A =~ 3.8 degs --> 4 degs<BR>\n" );
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document.write( "The course = 090 - 4 = 086<BR>\n" );
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document.write( "Note:  East is 090 degs heading, and the angles increase clockwise<BR>\n" );
document.write( "The plane is flying a heading of 090 @ 160 knots<BR>\n" );
document.write( "Winds are 240 @ 24 kts.<BR>\n" );
document.write( "\"Winds are two-four-zero at two-four.\" is what is said.<BR>\n" );
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