document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1022497>Question 1022497</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane is flying 215 miles per hour toward the Southeast (Theta Angle is 315 degrees).  A wind suddenly blows at 75 miles per hour from the North to the South (Theta Angle is 270 degrees).  Remember you will have to find the X-components & Y-components of the plane and wind.\r<BR>\n" );
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document.write( "New velocity of plane\r<BR>\n" );
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document.write( "Angle Alpha is \r<BR>\n" );
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document.write( "Angle Theta is<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638160 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=638160\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A plane is flying 215 miles per hour toward the Southeast (Theta Angle is 315 degrees).  A wind suddenly blows at 75 miles per hour from the North to the South (Theta Angle is 270 degrees).  Remember you will have to find the X-components & Y-components of the plane and wind.\r<BR>\n" );
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document.write( "New velocity of plane\r<BR>\n" );
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document.write( "Angle Alpha is \r<BR>\n" );
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document.write( "Angle Theta is<BR>\n" );
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document.write( "In aviation (and other navigation) North is 0/360 degs, and angles are measured clockwise.<BR>\n" );
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document.write( "The plane's heading is 135 degs.<BR>\n" );
document.write( "The wind is 360 @ 75.<BR>\n" );
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document.write( "Draw a triangle with a leg of length 215 (the speed) at 135 degs.<BR>\n" );
document.write( "From the lower right end, draw a vertical line of length 75 (windspeed).<BR>\n" );
document.write( "The angle between the 2 legs is 135 degs.<BR>\n" );
document.write( "Use the Cosine Law to find the 3rd side (the resultant ground speed).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2+%2B+b%5E2+-+2ab%2Acos%28135%29 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2+%2B+b%5E2+-+2ab%2Acos%28135%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+215%5E2+%2B+75%5E2+-+2%2A215%2A75%2A%28-sqrt%282%29%2F2%29 ALIGN=MIDDLE  ALT=\"c%5E2+=+215%5E2+%2B+75%5E2+-+2%2A215%2A75%2A%28-sqrt%282%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+74654.194 ALIGN=MIDDLE  ALT=\"c%5E2+=+74654.194\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c =~ 273.23 mi/hr (the groundspeed)<BR>\n" );
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document.write( "Call the angle between the plane's heading and its ground track A:<BR>\n" );
document.write( "Use the Sine Law:<BR>\n" );
document.write( "sin(A)/75 = sin(135)/273.23<BR>\n" );
document.write( "sin(A) =~ 0.194<BR>\n" );
document.write( "A = 11.19 degs<BR>\n" );
document.write( "--> ground track = 146.19 degs<BR>\n" );
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document.write( "Angle on the x-y plane = 303.8 degs\r<BR>\n" );
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document.write( "The ground track = 135 + angle A<BR>\n" );
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document.write( "It's not clear what angles alpha and theta are located.<BR>\n" );
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document.write( "PS  Pilots don't do trig, they use computers of various types to do it for them. </SPAN>\n" );
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