document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159987>Question 1159987</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two forces act on an object at 30° to each other. One force has a magnitude of 180 N, and the resultant has a magnitude of 320 N. a) Draw a vector diagram illustrating this situation.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #783471 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=783471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The magnitude of the resultant of the twp forces,  in Newton, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=320 ALIGN=MIDDLE  ALT=\"R=320\"   DISABLED_style= \"max-width:90%; height:auto;\" > .The magnitude of a known first force, in Newton, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F1=180 ALIGN=MIDDLE  ALT=\"F1=180\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Let the magnitude of the second force be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F2 ALIGN=MIDDLE  ALT=\"F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Newton.<BR>\n" );
document.write( "I would draw my vector diagram as shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28650%2C240%2C-10%2C315%2C-10%2C100%2C%0D%0Aline%280%2C0%2C151.2%2C0%29%2C%0D%0Aarrow%28100%2C0%2C151.2%2C0%29%2C%0D%0Aline%28151.2%2C0%2C307.08%2C90%29%2C%0D%0Aarrow%28255.12%2C60%2C307.08%2C90%29%2C%0D%0Aarrow%28151.2%2C0%2C350%2C0%29%2C%0D%0Ared%28line%280%2C0%2C307.08%2C90%29%29%2C%0D%0Ared%28arrow%28204.72%2C60%2C307.08%2C90%29%29%2C%0D%0Agreen%28arc%28151.2%2C0%2C60%2C60%2C-30%2C0%29%29%2C%0D%0Alocate%28180%2C15%2Cgreen%2830%5Eo%29%29%2C%0D%0Alocate%2875%2C0%2CF2%29%2C+locate%28150%2C45%2Cred%28R%29%29%2C%0D%0Alocate%28230%2C45%2CF1%29%0D%0A%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Depending on instructor preferences, the diagram expected could have<BR>\n" );
document.write( "both vectors starting from the same point with parallel segments added forming a parallelogram, like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28650%2C240%2C-10%2C315%2C-10%2C100%2C%0D%0Aline%280%2C0%2C151.2%2C0%29%2C%0D%0Aarrow%28100%2C0%2C151.2%2C0%29%2C%0D%0Atriangle%28151.2%2C0%2C307.08%2C90%2C0%2C0%29%2C%0D%0Atriangle%28155.88%2C90%2C307.08%2C90%2C0%2C0%29%2C%0D%0Aarrow%28103.92%2C60%2C155.88%2C90%29%2C%0D%0Aline%280%2C0%2C155.88%2C90%29%2C%0D%0Ared%28line%280%2C0%2C307.08%2C90%29%29%2C%0D%0Ared%28arrow%28204.72%2C60%2C307.08%2C90%29%29%2C%0D%0Agreen%28arc%280%2C0%2C60%2C60%2C-30%2C0%29%29%2C%0D%0Alocate%2830%2C12%2Cgreen%2830%5Eo%29%29%2C%0D%0Alocate%2875%2C0%2CF2%29%2C+locate%28150%2C45%2Cred%28R%29%29%2C%0D%0Alocate%2878%2C45%2CF1%29%0D%0A%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "I could solve it several different ways,<BR>\n" );
document.write( "but here is a simple way, assuming knowing only a little trigonometry.<BR>\n" );
document.write( "We are concerned with two right triangles, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC ALIGN=MIDDLE  ALT=\"ABC\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABD ALIGN=MIDDLE  ALT=\"ABD\"   DISABLED_style= \"max-width:90%; height:auto;\" > below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28650%2C240%2C-10%2C315%2C-10%2C100%2C%0D%0Atriangle%28151.2%2C0%2C307.08%2C90%2C0%2C0%29%2C%0D%0Atriangle%28307.08%2C0%2C307.08%2C90%2C0%2C0%29%2C%0D%0Ared%28line%280%2C0%2C307.08%2C90%29%29%2C%0D%0Agreen%28arc%28151.2%2C0%2C60%2C60%2C-30%2C0%29%29%2C%0D%0Alocate%28180%2C15%2Cgreen%2830%5Eo%29%29%2C%0D%0Alocate%2875%2C0%2CF2%29%2C+locate%28150%2C45%2Cred%28R%29%29%2C%0D%0Alocate%28230%2C45%2CF1%29%2Clocate%28-2%2C0%2CA%29%2C%0D%0Alocate%28308%2C95%2CB%29%2Clocate%28151%2C0%2CC%29%2Clocate%28307%2C0%2CD%29%0D%0A%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=320 ALIGN=MIDDLE  ALT=\"AB=320\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the magnitude of R)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=180 ALIGN=MIDDLE  ALT=\"BC=180\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the magnitude of F1)<BR>\n" );
document.write( "We want to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC ALIGN=MIDDLE  ALT=\"AC\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the magnitude of F2).<BR>\n" );
document.write( "From trigonometry, we find that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD=180%2Acos%2830%5Eo%29=155.88 ALIGN=MIDDLE  ALT=\"CD=180%2Acos%2830%5Eo%29=155.88\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD=180%2Asin%2830%5Eo%29=90 ALIGN=MIDDLE  ALT=\"BD=180%2Asin%2830%5Eo%29=90\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We can find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD ALIGN=MIDDLE  ALT=\"AD\"   DISABLED_style= \"max-width:90%; height:auto;\" > simply using the Pythagorean theorem as<BR>\n" );
document.write( "In physics class you could say those are the magnitudes of the horizontal and vertical components of F1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD=sqrt%28AB%5E2%2BBD%5E2%29=sqrt%28320%5E2-90%5E2%29=307.08 ALIGN=MIDDLE  ALT=\"AD=sqrt%28AB%5E2%2BBD%5E2%29=sqrt%28320%5E2-90%5E2%29=307.08\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You could say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD+is+the+magnitude+of+the+horizontal+component+of+R.%0D%0AWith+%7B%7B%7BAD ALIGN=MIDDLE  ALT=\"AD+is+the+magnitude+of+the+horizontal+component+of+R.%0D%0AWith+%7B%7B%7BAD\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD ALIGN=MIDDLE  ALT=\"CD\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we find<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=AD-CD=307.08-155.88=151.2 ALIGN=MIDDLE  ALT=\"AC=AD-CD=307.08-155.88=151.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );