document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83146>Question 83146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two tow trucks try to pull a car out of a ditch.One tow truck applies a force of 1,500 pounds while the other truck applies a force of 2,000 pounds. The resultant force is 3,000 pounds. Find the anlge between the two forces, rounded to the nearest degree.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60032 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=60032\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two tow trucks try to pull a car out of a ditch.One tow truck applies a force<BR>\n" );
document.write( "of 1,500 pounds while the other truck applies a force of 2,000 pounds. The<BR>\n" );
document.write( "resultant force is 3,000 pounds. Find the anlge between the two forces, rounded<BR>\n" );
document.write( "to the nearest degree.\r<BR>\n" );
document.write( "\n" );
document.write( "Draw the two vector forces and their resultant and the parallelogram:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28400%2C200%2C-3%2C3%2C-1%2C2%2C+line%280%2C0%2C2%2C0%29%2C+line%280%2C0%2C.6875%2C1.333%29%2C+%0D%0A+++line%28.7%2C1.2%2C.6875%2C1.333%29%2Cline%28.5%2C1.2%2C.6875%2C1.333%29%2C+line%282.6875%2C1.333%2C0%2C0%29%2C+%0D%0A+++line%281.8%2C.1%2C2%2C0%29%2Cline%281.8%2C-.1%2C2%2C0%29%2Cline%28.6875%2C1.333%2C2.6875%2C1.333%29%2C+%0D%0A+++line%282.4%2C1.1%2C2.6875%2C1.3333%29%2C+line%282.35%2C1.25%2C2.6875%2C1.3333%29%2C+%0D%0A+++locate%281.2%2C.6%2C%223000%23%22%29%2C%0D%0A+++locate%28-.3%2C1%2C%221500%23%22%29%2C+locate%28.8%2C-.15%2C%222000%23%22%29%2C+line%282%2C0%2C2.6875%2C1.333%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Isolate the upper triangle and label it ABC with sides a,b, and c::<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28400%2C+200%2C-3%2C3%2C-1%2C2%2C++line%280%2C0%2C.6875%2C1.333%29%2C+%0D%0A+++line%282.6875%2C1.333%2C0%2C0%29%2C+line%28.6875%2C1.333%2C2.6875%2C1.333%29%2C+%0D%0A+++locate%28.6%2C1.6%2CA%29%2C+locate%282.6%2C1.6%2CB%29%2C%0D%0A+++locate%281.2%2C.6%2C%22a=3000%22%29%2C%0D%0A+++locate%28-.3%2C1%2C%22b=1500%22%29%2C+locate%28.99%2C1.6%2C%22c=2000%22%29%2C+locate%28-.1%2C-.1%2CC%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Solve for angle A using the law of cosines \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+b%5E2+%2B+c%5E2+-+2bc%2Acos%28A%29 ALIGN=MIDDLE  ALT=\"a%5E2+=+b%5E2+%2B+c%5E2+-+2bc%2Acos%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2bc%2Acos%28A%29=b%5E2%2Bc%5E2-a%5E2 ALIGN=MIDDLE  ALT=\"2bc%2Acos%28A%29=b%5E2%2Bc%5E2-a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28A%29=%28b%5E2%2Bc%5E2-a%5E2%29%2F%282bc%29 ALIGN=MIDDLE  ALT=\"cos%28A%29=%28b%5E2%2Bc%5E2-a%5E2%29%2F%282bc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28A%29=%281500%5E2%2B2000%5E2-3000%5E2%29%2F%282%2A1500%2A2000%29 ALIGN=MIDDLE  ALT=\"cos%28A%29=%281500%5E2%2B2000%5E2-3000%5E2%29%2F%282%2A1500%2A2000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28A%29=-2750000%2F6000000 ALIGN=MIDDLE  ALT=\"cos%28A%29=-2750000%2F6000000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28A%29+=+-.4583333333 ALIGN=MIDDLE  ALT=\"cos%28A%29+=+-.4583333333\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Find the inverse cosine:\r<BR>\n" );
document.write( "\n" );
document.write( "     A = 117° to nearest degree\r<BR>\n" );
document.write( "\n" );
document.write( "Now back to the vector drawing:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28400%2C200%2C-3%2C3%2C-1%2C2%2C+line%280%2C0%2C2%2C0%29%2C+line%280%2C0%2C.6875%2C1.333%29%2C+%0D%0A+++line%28.7%2C1.2%2C.6875%2C1.333%29%2Cline%28.5%2C1.2%2C.6875%2C1.333%29%2C+line%282.6875%2C1.333%2C0%2C0%29%2C+%0D%0A+++line%281.8%2C.1%2C2%2C0%29%2Cline%281.8%2C-.1%2C2%2C0%29%2Cline%28.6875%2C1.333%2C2.6875%2C1.333%29%2C+%0D%0A+++line%282.4%2C1.1%2C2.6875%2C1.3333%29%2C+line%282.35%2C1.25%2C2.6875%2C1.3333%29%2C+%0D%0A+++locate%281.2%2C.6%2C%223000%23%22%29%2Clocate%28.6%2C1.2%2C%22117%B0%22%29%2C+%0D%0A+++locate%28-.3%2C1%2C%221500%23%22%29%2C+locate%28.8%2C-.15%2C%222000%23%22%29%2C+line%282%2C0%2C2.6875%2C1.333%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Angle A, however, is not the angle between the forces.  But we notice by<BR>\n" );
document.write( "removing the resultant 3000# vector:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28400%2C200%2C-3%2C3%2C-1%2C2%2C+line%280%2C0%2C2%2C0%29%2C+line%280%2C0%2C.6875%2C1.333%29%2C+%0D%0A+++line%28.7%2C1.2%2C.6875%2C1.333%29%2Cline%28.5%2C1.2%2C.6875%2C1.333%29%2C+%0D%0A+++line%281.8%2C.1%2C2%2C0%29%2Cline%281.8%2C-.1%2C2%2C0%29%2Cline%28.6875%2C1.333%2C2.6875%2C1.333%29%2C+%0D%0A++++%0D%0A+++locate%28.6%2C1.2%2C%22117%B0%22%29%2C+%0D%0A+++locate%28-.3%2C1%2C%221500%23%22%29%2C+locate%28.8%2C-.15%2C%222000%23%22%29%2C+line%282%2C0%2C2.6875%2C1.333%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "that, since two adjacent angles of a parallelogram are supplementary,<BR>\n" );
document.write( "we only need to subtract 117° from 180° and get 63°, the angle between<BR>\n" );
document.write( "the two forces:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28400%2C200%2C-3%2C3%2C-1%2C2%2C+line%280%2C0%2C2%2C0%29%2C+line%280%2C0%2C.6875%2C1.333%29%2C+%0D%0A+++line%28.7%2C1.2%2C.6875%2C1.333%29%2Cline%28.5%2C1.2%2C.6875%2C1.333%29%2C+%0D%0A+++line%281.8%2C.1%2C2%2C0%29%2Cline%281.8%2C-.1%2C2%2C0%29%2Cline%28.6875%2C1.333%2C2.6875%2C1.333%29%2C+%0D%0A++++%0D%0A+++locate%28.6%2C1.2%2C%22117%B0%22%29%2C+locate%28.2%2C.3%2C%2263%B0%22%29%2C+%0D%0A+++locate%28-.3%2C1%2C%221500%23%22%29%2C+locate%28.8%2C-.15%2C%222000%23%22%29%2C+line%282%2C0%2C2.6875%2C1.333%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28400%2C200%2C-3%2C3%2C-1%2C2%2C+line%280%2C0%2C2%2C0%29%2C+line%280%2C0%2C.6875%2C1.333%29%2C+%0D%0A+++line%28.7%2C1.2%2C.6875%2C1.333%29%2Cline%28.5%2C1.2%2C.6875%2C1.333%29%2C+%0D%0A+++line%281.8%2C.1%2C2%2C0%29%2Cline%281.8%2C-.1%2C2%2C0%29%2C++locate%28.2%2C.3%2C%2263%B0%22%29%2C+%0D%0A+++locate%28-.3%2C1%2C%221500%23%22%29%2C+locate%28.8%2C-.15%2C%222000%23%22%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Edwin</pre> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );