document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=714767>Question 714767</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Describe the resultant as an ordered pair\r<BR>\n" );
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document.write( "a canoe heading 30 degrees west of north is being paddled at a rate of 7 mi/hr. The current is pushing the canoe 20 degrees south of west at a rate of 3 mi/hr. Find the resulting speed and direction of the canoe.\r<BR>\n" );
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document.write( "I dont understand how to set up this problem and have know idea what to do. Please, if you can not graph it, then can you say the steps clearly? Alrighty...<BR>\n" );
document.write( "THanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #439137 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=439137\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-8%2C2%2C-2%2C8%2C%0D%0Agrid%280%29%2Clocate%280.1%2C0.6%2CO%29%2C%0D%0Ared%28arrow%281%2C1%2C1%2C4%29%29%2Clocate%280.9%2C4.6%2Cred%28N%29%29%2C%0D%0Ablue%28line%280%2C0%2C-3.5%2C6.062%29%29%2Cblue%28arrow%28-2%2C3.464%2C-3.5%2C6.062%29%29%2C%0D%0Ablue%28arrow%280%2C0%2C-2.819%2C-1.026%29%29%2C%0D%0Acircle%28-3.5%2C6.062%2C0.1%29%2Clocate%28-3.6%2C6.6%2CA%29%2C%0D%0Acircle%28-2.819%2C-1.026%2C0.1%29%2Clocate%28-2.9%2C-1.07%2CB%29%2C%0D%0Acircle%28-6.319%2C5.036%2C0.1%29%2Clocate%28-6.4%2C5.6%2CC%29%2C%0D%0Ablue%28line%280%2C0%2C-6.319%2C5.036%29%29%2Cblue%28arrow%28-3.91%2C3.116%2C-6.319%2C5.036%29%29%2C%0D%0Agreen%28line%28-3.5%2C6.062%2C-6.319%2C5.036%29%29%2C%0D%0Agreen%28line%28-2.9%2C-1.07%2C-6.319%2C5.036%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Arrow OB, with length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , represents the current velocity.<BR>\n" );
document.write( "Arrow OA, with length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > , represents the paddling velocity (relative to the water).<BR>\n" );
document.write( "They add up to yield arrow OC, representing the canoe's velocity (relative to the ground).<BR>\n" );
document.write( "OA makes an angle of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5Eo ALIGN=MIDDLE  ALT=\"30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the positive y-axis,<BR>\n" );
document.write( "so the coordinates of A are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BA%5D=-7%2Asin%2830%5Eo%29=-7%2A0.5=-3.5 ALIGN=MIDDLE  ALT=\"x%5BA%5D=-7%2Asin%2830%5Eo%29=-7%2A0.5=-3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5BA%5D=7%2Acos%2830%5Eo%29=7%2A0.866=6.602 ALIGN=MIDDLE  ALT=\"y%5BA%5D=7%2Acos%2830%5Eo%29=7%2A0.866=6.602\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded values).<BR>\n" );
document.write( "OB makes an angle of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5Eo ALIGN=MIDDLE  ALT=\"20%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the negative x-axis,<BR>\n" );
document.write( "so the coordinates of B are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BB%5D=-3%2Acos%2820%5Eo%29=-3%2A0.9396=-2.819 ALIGN=MIDDLE  ALT=\"x%5BB%5D=-3%2Acos%2820%5Eo%29=-3%2A0.9396=-2.819\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5BB%5D=-3%2Asin%2820%5Eo%29=-3%2A0.342=-1.026 ALIGN=MIDDLE  ALT=\"y%5BB%5D=-3%2Asin%2820%5Eo%29=-3%2A0.342=-1.026\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded values).<BR>\n" );
document.write( "The coordinates represent how far (in miles) the canoe would move in one hour<BR>\n" );
document.write( "to the East (for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and to the North (for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "under the influence of each velocity.<BR>\n" );
document.write( "We can represent those velocities (speed and direction)<BR>\n" );
document.write( "by those pairs of coordinates.<BR>\n" );
document.write( "The resultant speed is represented by the coordinates of point C<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BC%5D=x%5BA%5D%2Bx%5BB%5D=-3.5%2B%28-2.819%29=-6.319 ALIGN=MIDDLE  ALT=\"x%5BC%5D=x%5BA%5D%2Bx%5BB%5D=-3.5%2B%28-2.819%29=-6.319\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5BC%5D=y%5BA%5D%2By%5BB%5D=6.602%2B%28-1.026%29=5.036 ALIGN=MIDDLE  ALT=\"y%5BC%5D=y%5BA%5D%2By%5BB%5D=6.602%2B%28-1.026%29=5.036\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The coordinates of C are the ordered pair (-6.319, 5.036), which represents the velocity of the canoe with respect to the ground.<BR>\n" );
document.write( "From those coordinates we can find<BR>\n" );
document.write( "the length of OC, which represents the resultant speed,<BR>\n" );
document.write( "and the angle OC makes with the positive y-axis which tells us the direction.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=speed=sqrt%286.319%5E2%2B5.036%5E2%29=highlight%288.08%29 ALIGN=MIDDLE  ALT=\"speed=sqrt%286.319%5E2%2B5.036%5E2%29=highlight%288.08%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The speed is about 8 mph.<BR>\n" );
document.write( "The angle of OC with the the positive y-axis tells us the direction as an angle West of North<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28angle%29=6.319%2F5.036=1.2548 ALIGN=MIDDLE  ALT=\"tan%28angle%29=6.319%2F5.036=1.2548\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=angle=highlight%2851.4%5Eo%29 ALIGN=MIDDLE  ALT=\"angle=highlight%2851.4%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The direction is about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=51.4%5Eo ALIGN=MIDDLE  ALT=\"51.4%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > West of North.<BR>\n" );
document.write( "That's the angle the direction forms with the North direction. </SPAN>\n" );
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