document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=979889>Question 979889</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this vectors problem:\r<BR>\n" );
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document.write( "Given vectors of magnitude 3 and 4 with an angle between them of 80°, find the magnitude of the resultant. <BR>\n" );
document.write( "Enter answer accurate to two decimal places.\r<BR>\n" );
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document.write( "Thank you in advanced. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601131 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52832)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Resultant is the sum of given vectors, &nbsp;correct? \r<BR>\n" );
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document.write( "The sum of vectors is the diagonal of a parallelogram built on these vectors. &nbsp;Do you know it? &nbsp;See the &nbsp;<B>Figure</B>&nbsp; below.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+242%2C+200%2C+-6.0%2C+6.1%2C+-4.0%2C+5.0%2C%0D%0A++++++++++++line%28-5.0%2C+-3.0%2C+-2.0%2C+1.0%29%2C%0D%0A++++++++++++locate+%28-5.2%2C++-3.0%2C+A%29%2C+%0D%0A++++++++++++locate+%28-2.4%2C+++1.7%2C+B%29%2C%0D%0A++++++++++++line%28+-2.0%2C+1.0%2C+-2.5%2C+0.7%29%2C%0D%0A++++++++++++line%28+-2.0%2C+1.0%2C+-2.1%2C+0.5%29%2C%0D%0A%0D%0A%0D%0A++++++++++++line%28-2.0%2C+1.0%2C+4.0%2C+2.0%29%2C%0D%0A++++++++++++locate+%284.1%2C+++2.5%2C+C%29%2C+%0D%0A%0D%0A%0D%0A++++++++red%28line%28-5.0%2C+-3.0%2C+4.0%2C+2.0%29%29%2C%0D%0A++++++++++++line%28+4.0%2C+2.0%2C++3.5%2C+1.57%29%2C+%0D%0A++++++++++++line%28+4.0%2C+2.0%2C++3.3%2C+1.80%29%2C+%0D%0A%0D%0A++++++++++++line%28-5.0%2C+-3.0%2C+1.0%2C+-2.0%29%2C%0D%0A++++++++++++locate+%281.1%2C++-1.9%2C+D%29%2C%0D%0A++++++++++++line%28+1.0%2C+-2.0%2C++0.5%2C+-1.85%29%2C%0D%0A++++++++++++line%28+1.0%2C+-2.0%2C++0.5%2C+-2.25%29%2C%0D%0A%0D%0A++++++++++++line%281.0%2C+-2.0%2C+4.0%2C+2.0%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "&nbsp;&nbsp;<B>Figure</B>. &nbsp;The sum of the vectors&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<BR>\n" );
document.write( "<B>AB</B> + <B>AD</B> = <B>AC</B> &nbsp;(the &nbsp;<B>parallelogram rule</B>)<BR>\n" );
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document.write( "So, &nbsp;we are given the vectors &nbsp;<B>AB</B>&nbsp; and &nbsp;<B>AD</B>&nbsp; of the length &nbsp;3&nbsp; and &nbsp;4&nbsp; and the angle &nbsp;<I>L</I><B>A</B> = 80°&nbsp; between them. \r<BR>\n" );
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document.write( "The magnitude of the resultant is the length of the vector of sum, &nbsp;which is the vector &nbsp;<B>AC</B>.\r<BR>\n" );
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document.write( "Apply the &nbsp;<B>Law of Cosines</B>&nbsp; (see the lesson &nbsp;<A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Trigonometry-basics/Proof-of-the-Law-of-Cosines-revisited.lesson>Proof of the Law of Cosines revisited</A>&nbsp; in this site)&nbsp; to the triangle &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA ALIGN=MIDDLE  ALT=\"DELTA\"   DISABLED_style= \"max-width:90%; height:auto;\" ></B>ADC</B>&nbsp; to find the measure of its side &nbsp;<B>AC</B>.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28AC%29%5E2 ALIGN=MIDDLE  ALT=\"abs%28AC%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28AD%29%5E2 ALIGN=MIDDLE  ALT=\"abs%28AD%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28DC%29%5E2 ALIGN=MIDDLE  ALT=\"abs%28DC%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aabs%28AD%29%2Aabs%28DC%29%2Acos%28D%29 ALIGN=MIDDLE  ALT=\"2%2Aabs%28AD%29%2Aabs%28DC%29%2Acos%28D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3^2 + 4^2 - 2*3*4*cos(100°) = 9 + 16 - 24*(-0.17365) = 29.16752.\r<BR>\n" );
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document.write( "Hence, &nbsp;|<B>AC</B>| = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2829.16752%29 ALIGN=MIDDLE  ALT=\"sqrt%2829.16752%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5.40. \r<BR>\n" );
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document.write( "<B>Answer</B>. &nbsp;The magnitude of the resultant is &nbsp;5.40. \r<BR>\n" );
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