document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102869>Question 1102869</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <p>Two forces <strong>429 N</strong> and <strong>591 N</strong> act on an object. The angle between the forces is <strong>46&deg;</strong>. Find the <span  DISABLED_style= \"text-decoration: underline;\">magnitude of the resultant</span> and the <span  DISABLED_style= \"text-decoration: underline;\">angle that it makes with the larger force</span>.</p><BR>\n" );
document.write( "<p>Thank you friends</p> </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717599 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=717599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is a representation of the two forces and their resultant,<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C300%2C-100%2C900%2C-100%2C400%2C%0D%0Agrid%280%29%2Cline%280%2C0%2C591%2C0%29%2Carrow%280%2C0%2C591%2C0%29%2C%0D%0Aline%28591%2C0%2C889%2C308.6%29%2Carrow%28591%2C0%2C889%2C308.6%29%2C%0D%0Aline%280%2C0%2C889%2C308.6%29%2Carrow%28444.5%2C154.3%2C889%2C308.6%29%2C%0D%0Alocate%28300%2C30%2C591N%29%2Clocate%28444.5%2C154.3%2CR%29%2C%0D%0Alocate%28740%2C154.3%2C429N%29%2Clocate%28620%2C50%2C46%5Eo%29%2C%0D%0Ared%28arc%28591%2C0%2C200%2C200%2C-46%2C0%29%29%2Clocate%28150%2C40%2Ctheta%29%2C%0D%0Ared%28arc%280%2C0%2C400%2C400%2C-19.1%2C0%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The rest is trigonometry.<BR>\n" );
document.write( "You could use law of cosines and law of sines,<BR>\n" );
document.write( "but I would favor just calculating the horizontal and vertical components.<BR>\n" );
document.write( "The 429N force can be seen as the sum of<BR>\n" );
document.write( "a horizontal component of magnitude <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2846%5Eo%29%2A429N=about+298.0N ALIGN=MIDDLE  ALT=\"cos%2846%5Eo%29%2A429N=about+298.0N\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "a vertical component of magnitude <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2846%5Eo%29%2A429N=about+308.6N ALIGN=MIDDLE  ALT=\"sin%2846%5Eo%29%2A429N=about+308.6N\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The 591N force an be seen as the sum of<BR>\n" );
document.write( "a horizontal component of magnitude <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=591N ALIGN=MIDDLE  ALT=\"591N\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "a vertical component of magnitude <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0N ALIGN=MIDDLE  ALT=\"0N\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Adding up components, you get the horizontal and vertical components,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Bx%5D=298.0N%2B591N=889.0N ALIGN=MIDDLE  ALT=\"R%5Bx%5D=298.0N%2B591N=889.0N\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5By%5D=308.6N%2B0N=308.6N ALIGN=MIDDLE  ALT=\"R%5By%5D=308.6N%2B0N=308.6N\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=R%5By%5D%2FR%5Bx%5D=308.6N%2F%22740.0+N%22=0.3341 ALIGN=MIDDLE  ALT=\"tan%28theta%29=R%5By%5D%2FR%5Bx%5D=308.6N%2F%22740.0+N%22=0.3341\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=19.1%5Eo ALIGN=MIDDLE  ALT=\"theta=19.1%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=sqrt%28%28889.0N%29%5E2%2B%28308.6N%29%5E2%29=sqrt%28790336N%5E2%2B95232N%5E2%29=sqrt%28885568N%5E2%29=about941.0N ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );