document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=357331>Question 357331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane needs to fly to a town located 200 km away in the direction 50 degrees east of north. There is westerly wind blowing at 60 km/h.\r<BR>\n" );
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document.write( "Determine the plane's airspeed and the direction in the degrees east of north, so it can fly directly to the town in 1/2 hour.\r<BR>\n" );
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document.write( "Help me please with the question.\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #255206 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=255206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A plane needs to fly to a town located 200 km away in the direction 50 degrees east of north. There is westerly wind blowing at 60 km/h. <BR>\n" );
document.write( "Determine the plane's airspeed and the direction in the degrees east of north, so it can fly directly to the town in 1/2 hour. <BR>\n" );
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document.write( "The groundspeed has to be 400 km/hr (200 km/0.45 hr)<BR>\n" );
document.write( "The wind is 60 from the west.<BR>\n" );
document.write( "The angle between the flight path and the wind direction is 40º where they meet at the town.<BR>\n" );
document.write( "This makes a triangle with sides meeting at the town of 400 and 60 with the angle between them of 40º.<BR>\n" );
document.write( "Use the Cosine Law to find the 3rd side, with is the plane's airspeed.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+60%5E2+%2B+400%5E2+-+2%2A60%2A400%2Acos%2840%29 ALIGN=MIDDLE  ALT=\"a%5E2+=+60%5E2+%2B+400%5E2+-+2%2A60%2A400%2Acos%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+126830 ALIGN=MIDDLE  ALT=\"a%5E2+=+126830\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "airspeed = 356.13 km/hr<BR>\n" );
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document.write( "Use the Law of Sines to find the heading of the plane:<BR>\n" );
document.write( "356.13/sin(40) = 60/sin(B)<BR>\n" );
document.write( "sin(B) = 60*sin(40)/356.13 = 0.10829<BR>\n" );
document.write( "B = 6.217º<BR>\n" );
document.write( "Heading = 50 - B = 43.8º<BR>\n" );
document.write( "or 43.8 East of North<BR>\n" );
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document.write( "PS  Wind info is always given as the direction it's from.<BR>\n" );
document.write( "A \"westerly wind\" of 10 knots would be given as \"winds 270 at 10\"<BR>\n" );
document.write( "West is 270, and 10 is the windspeed in knots.<BR>\n" );
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