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?

Expert Solution

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 )

54.9°

Nipun Maity answered 3 years ago

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