document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=813233>Question 813233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane leaves an airport and travels 2500 mi. due West, then turns 38 degrees to the south and travels 240 mi to a second airport.  What is the displacement of the 1st airport from the 2nd airport? Round to 3 decimal places.  It asks for Magnitude and Direction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #489562 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=489562\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> use the law of cosines to find the third side of the triangle<BR>\n" );
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document.write( "a^2 = b^2 + c^2 - 2bc cos(I)<BR>\n" );
document.write( "where:<BR>\n" );
document.write( "b = 2500<BR>\n" );
document.write( "c = 240<BR>\n" );
document.write( "---<BR>\n" );
document.write( "but first find the included angle I<BR>\n" );
document.write( "I = 180 - 38 = 142 degrees<BR>\n" );
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document.write( "a^2 = 2500^2 + 240^2 - 2*2500*240*cos(142)<BR>\n" );
document.write( "a^2 = 6.25e6 + 5.76e4 - 1.2e6*(-0.7880107)<BR>\n" );
document.write( "a^2 = 6.25e6 + 5.76e4 + 9.456129e5<BR>\n" );
document.write( "a^2 = 7.2532129e6<BR>\n" );
document.write( "a = 2693.179<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the airplane arrives at ap2 at a distance of 2693.179 miles from ap1.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "now use the law of sines to find the smaller angle J of the triangle (ap1, turn-point, ap2):<BR>\n" );
document.write( "sin(J)/j = sin(I)/i<BR>\n" );
document.write( "sin(J)/240 = sin(142)/2693.179<BR>\n" );
document.write( "sin(J)= sin(142)240/2693.179<BR>\n" );
document.write( "sin(J)= (0.6156614)240/2693.179<BR>\n" );
document.write( "sin(J)= 0.054864<BR>\n" );
document.write( "J = arcsin(0.054864)<BR>\n" );
document.write( "J = 3.1450587 degrees<BR>\n" );
document.write( "---<BR>\n" );
document.write( "direction from ap2 to ap1 is:<BR>\n" );
document.write( "90 - 3.1450587 = 86.854941 ~= 86.855 degrees true north bearing<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "the vector from ap2 to ap1 is:<BR>\n" );
document.write( "Direction: 86.855 degrees true north<BR>\n" );
document.write( "Magnitude: 2693.179 miles<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Convert fractions, decimals, and percents:<BR>\n" );
document.write( "https://sooeet.com/math/fraction-decimal-percent.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Calculate and graph the linear regression of any data set:<BR>\n" );
document.write( "https://sooeet.com/math/linear-regression.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );