Roman C. answered • 12/02/12

Masters of Education Graduate with Mathematics Expertise

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.

125^{2} = 55^{2} + 85^{2} - 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 )

Daniel 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:

tail-to-tail:

http://pad1.whstatic.com/images/thumb/a/a3/Find-the-Angle-Between-Two-Vectors-Step-1.jpg/550px-Find-the-Angle-Between-Two-Vectors-Step-1.jpg

nose-to-tail:

http://www.onlinemathlearning.com/image-files/vector-addition4.gif

12/03/12