Question

Two forces of 2 Newton and 3 Newton act at a point so as to produce a resultant force of 4 Newton .Find:
a. The angle between the directions of the 2 Newton and 3 Newton forces
b.the angle between the directions of the resultant and the 3 newton force

Answer 1

2 from (0,0), point A to (2,0), point C
3 from (0,0) to (x,y)
line parallel to that of length 3 to point B to make parallelogram

cosines:
4^2 = 3^2 + 2^2 - 2(6) cos C
where C is angle at C inside parallelogram
so
cos C = -.25
C = 104.5 degrees

so our angle from x axis to B is 180-104 = 75.5
That is angle between 2 and 3 N forces

now angle A between 4 and 2
sin A/3 = sin C/4
sin A / 3 = .968 /4
sin A = .726
A = 46.6 degrees