document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=813578>Question 813578</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boat is traveling 12 mph on a compass bearing of 180 degrees. There is a current of four mph flowing from east to west. What is the actual speed and direction of the boat relative to dry land? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #489847 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=489847\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> use vector velocities:<BR>\n" );
document.write( "b: magnitude = 12, direction = 180 degrees<BR>\n" );
document.write( "w: magnitude = 4, direction = 270 degrees<BR>\n" );
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document.write( "we want the vector sum: <BR>\n" );
document.write( "v = b + w<BR>\n" );
document.write( "---<BR>\n" );
document.write( "because the vectors are perpendicular, we can use the pythagorean theorem for the magnitude of v:<BR>\n" );
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document.write( "magnitude of v:<BR>\n" );
document.write( "M(v) = sqrt( bb + ww )<BR>\n" );
document.write( "M(v) = sqrt( 144 + 16 )<BR>\n" );
document.write( "M(v) = 12.649111<BR>\n" );
document.write( "---<BR>\n" );
document.write( "direction of v:<BR>\n" );
document.write( "for the direction of v we need the small angle (A) of the right triangle:<BR>\n" );
document.write( "tan(A) = opp/adj = 4/12 = 1/3<BR>\n" );
document.write( "A = arctan(1/3) = 18.434949 degrees<BR>\n" );
document.write( "D(v) = 180 + 18.434949 = 198.434949 degrees<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "from dry land the boat will appear to be moving on a bearing and speed of: <BR>\n" );
document.write( "198.4 degrees at 12.7 mph<BR>\n" );
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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" );
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