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## Two forces of 55N and 85N act on an object simultaneously and the resultant force is 125N. What is the measurement of the angle between the two forces?

Use law of cosine,

1252 = 552 + 852 - 2*55*85cos(θ)

Solve for θ,

θ = 125.09 o

Shouldn't the angle between them be: 180 - 125.09? 125 degrees is the angle between them if you placed the force vectors nose-to-tail, but that isn't what I'd consider to be the angle between two vectors; it should be the angle between them when they're tail-to-tail.

Diana, see these diagrams if you're confused by what I mean:

Dear Robert.J.

Your calculation is quite right. But should we have to reconsider the angle between the two vectors ? I think it should be a suplement of the calculated angle.

Sung

Yes, you are correct. I used head to tail picture to get angle between the two sides, but not between the two forces.

The angle between the two vectors should be the supplement angle of what I calculated.

Denote the angle by θ.

Start with a parallelogram rule. The sum vector is along the diagonal of the parallelogram, splitting the parallelogram into two triangle with sides of lengths 55, 85, and 125. The angle opposite to the side of length 125 is π - θ radians. Now apply the law of cosines to finish.

1252 = 552 + 852 - 2*55*85 cos(π - θ)

15625 = 3025 + 7225 - 9350 cos(π - θ)

cos(π - θ) = 5375/9350 = -215/374

cos θ = 215/374

θ = 0.95835 radians ( 54.90972 degrees )