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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?

### 2 Answers by Expert Tutors

Roman C. | Masters of Education Graduate with Mathematics ExpertiseMasters of Education Graduate with Mathe...
4.9 4.9 (314 lesson ratings) (314)
2

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 )

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
1

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.