Question 615495
<pre>
Here's the complete solution:

Draw a little rectangle for the body, and sticking out of the body,
draw two vectors, one 3 units long for the 3 lb vector, and one 4
units long for the 4 lb vector, so that the angle between the two
vectors is 100°:

{{{drawing(1600/9,200,-2,6,-1,8,
red(arc(0,0,3.6,-3.6,0,100)), locate(.1,1,"100°"),
line(0,0,8cos(100*pi/180),8sin(100*pi/180)), line(0,0,6,0),
line(5.6,-.2,6,0),line(5.6,+.2,6,0), locate(2.3,0,3), locate(2.9,0,lb),
rectangle(-.3,-.2,.3,.2),
locate(-2,4,4), locate(-1.4,4,lb),
line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)-.1,8sin(100*pi/180)-.6),
line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)+.3,8sin(100*pi/180)-.5))
 )}}}

Next we complete the parallelogram, Through each arrowhead, draw
a line parallel to the other vector.  I'll draw them in green:

{{{drawing(1600/9,200,-2,6,-1,8,
red(arc(0,0,3.6,-3.6,0,100)), locate(.1,1,"100°"),
line(0,0,8cos(100*pi/180),8sin(100*pi/180)), line(0,0,6,0),
line(5.6,-.2,6,0),line(5.6,+.2,6,0), locate(2.3,0,3), locate(2.9,0,lb),
rectangle(-.3,-.2,.3,.2),
locate(-2,4,4), locate(-1.4,4,lb),
line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)-.1,8sin(100*pi/180)-.6),
line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)+.3,8sin(100*pi/180)-.5),
green(line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)+7,8sin(100*pi/180)),line(6,0,8cos(100*pi/180)+6,8sin(100*pi/180))  

)



 )}}}

The resultant of the two forces is a vector which is the diagonal of
the parallelogram from the body to the point where the two green lines
intersect, which I will draw in red

{{{drawing(1600/9,200,-2,6,-1,8,
red(arc(0,0,3.6,-3.6,0,100)), locate(.1,1,"100°"),
line(0,0,8cos(100*pi/180),8sin(100*pi/180)), line(0,0,6,0),
line(5.6,-.2,6,0),line(5.6,+.2,6,0), locate(2.3,0,3), locate(2.9,0,lb),
rectangle(-.3,-.2,.3,.2),
locate(-2,4,4), locate(-1.4,4,lb),
line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)-.1,8sin(100*pi/180)-.6),
line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)+.3,8sin(100*pi/180)-.5),
green(line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)+7,8sin(100*pi/180)),line(6,0,8cos(100*pi/180)+6,8sin(100*pi/180))),

red(line(0,0,8cos(100*pi/180)+6,8sin(100*pi/180)),
line(8cos(100*pi/180)+6,8sin(100*pi/180),8cos(100*pi/180)+5.3,8sin(100*pi/180)-.5), line(8cos(100*pi/180)+6,8sin(100*pi/180),8cos(100*pi/180)+5.8,8sin(100*pi/180)-.8)

)



 )}}}

Two adjacent angles of a parallelogram are supplementary so the angle
on the lower right is 180°-100° or 80°.

{{{drawing(1600/9,200,-2,6,-1,8,
red(arc(0,0,3.6,-3.6,0,100)), locate(.1,1,"100°"),
line(0,0,8cos(100*pi/180),8sin(100*pi/180)), line(0,0,6,0),
line(5.6,-.2,6,0),line(5.6,+.2,6,0), locate(2.3,0,3), locate(2.9,0,lb),
rectangle(-.3,-.2,.3,.2),
locate(-2,4,4), locate(-1.4,4,lb),
line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)-.1,8sin(100*pi/180)-.6),
line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)+.3,8sin(100*pi/180)-.5),
green(line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)+7,8sin(100*pi/180)),line(6,0,8cos(100*pi/180)+6,8sin(100*pi/180))),

red(line(0,0,8cos(100*pi/180)+6,8sin(100*pi/180)),
line(8cos(100*pi/180)+6,8sin(100*pi/180),8cos(100*pi/180)+5.3,8sin(100*pi/180)-.5), line(8cos(100*pi/180)+6,8sin(100*pi/180),8cos(100*pi/180)+5.8,8sin(100*pi/180)-.8)

),locate(4.7,1,"80°"),red(arc(6,0,3.6,-3.6,100,180)),

locate(-2+6.8,4,4), locate(-1.4+6.8,4,lb),
red(locate(2.6,4,R)) 



 )}}}

To find the magnitude of R, we use the law of cosines:

R² = a² + b² - 3·a·b·cos(<font face="symbol">phi</font>)
R² = 3² + 4² - 2(3)(4)cos(80°)
R² = 20.83244374
 R = 4.564257194 or to the nearest tenth of a pound, 
 R = 4.6 lb.

The angle between the 4 lb. vector and the resultant is either
of the two angles labeled <font face="symbol">q</font> below:
{{{drawing(1600/9,200,-2,6,-1,8,
red(arc(0,0,3.6,-3.6,0,100)), locate(.1,1,"100°"),
line(0,0,8cos(100*pi/180),8sin(100*pi/180)), line(0,0,6,0),
line(5.6,-.2,6,0),line(5.6,+.2,6,0), locate(2.3,0,3), locate(2.9,0,lb),
rectangle(-.3,-.2,.3,.2),
locate(-2,4,4), locate(-1.4,4,lb),
line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)-.1,8sin(100*pi/180)-.6),
line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)+.3,8sin(100*pi/180)-.5),
green(line(8cos(100*pi/180),8sin(100*pi/180),8cos(100*pi/180)+7,8sin(100*pi/180)),line(6,0,8cos(100*pi/180)+6,8sin(100*pi/180))),

red(line(0,0,8cos(100*pi/180)+6,8sin(100*pi/180)),
line(8cos(100*pi/180)+6,8sin(100*pi/180),8cos(100*pi/180)+5.3,8sin(100*pi/180)-.5), line(8cos(100*pi/180)+6,8sin(100*pi/180),8cos(100*pi/180)+5.8,8sin(100*pi/180)-.8)

),locate(4.7,1,"80°"),red(arc(6,0,3.6,-3.6,100,180)),

locate(-2+6.8,4,4), locate(-1.4+6.8,4,lb),
red(locate(2.6,4,R)),locate(4.2,7,theta), locate(0,2.5,theta) 



 )}}}

We'll get the <font face="symbol">q</font> at the top right
since we're working in that triangle. 

{{{R/sin("80°")}}} = {{{3/sin(theta)}}}

R·sin(<font face="symbol">q</font>) = 3·sin(80°)

sin(<font face="symbol">q</font>) = {{{3*sin("80°")/R}}}.

sin(<font face="symbol">q</font>) = {{{3*sin("80°")/4.564257194}}}.

sin(<font face="symbol">q</font>) = 0.6472955255

Use the inverse sine function on your calculator:

<font face="symbol">q</font> = 40.33800507°

or to the nearest degree, 40°.

Edwin</pre>