document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980592>Question 980592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve 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 100°, find the magnitude of the resultant.\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 #601719 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601719\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Draw the vectors where the tails are at the same point. The vectors are shown in blue. The resultant vector is shown in red.\r<BR>\n" );
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document.write( "Also, add in auxiliary lines to form a parallelogram. These are the black dashed lines.\r<BR>\n" );
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document.write( "Because we have a parallelogram, the adjacent angles are supplementary. So 100+x = 180 means x = 80 degrees. Also, the opposite sides of any parallelogram are congruent. All of this is shown below in the drawing.\r<BR>\n" );
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document.write( "The goal is to find the length of the red vector. To do this, we use the law of cosines <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2+%2B+b%5E2+-+2%2Aa%2Ab%2Acos%28C%29 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2+%2B+b%5E2+-+2%2Aa%2Ab%2Acos%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In this case, the sides of the triangle are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+3 ALIGN=MIDDLE  ALT=\"a+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+4 ALIGN=MIDDLE  ALT=\"b+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and 'c' is unknown. Angle C is 80 degrees. Solve for c to get...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2+%2B+b%5E2+-+2%2Aa%2Ab%2Acos%28C%29 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2+%2B+b%5E2+-+2%2Aa%2Ab%2Acos%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+4.564258 ALIGN=MIDDLE  ALT=\"c+=+4.564258\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The magnitude of the resultant is approximately <font color=\"red\">4.564258 units</font> long. </SPAN>\n" );
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