Question

When to input angles with positive or negative sign in calculation?

Yusef pushes a chair of mass m = 55.0 kg across a carpeted floor with a force F⃗ p (the subscript 'p' here is lowercase and throughout the question) of magnitude Fp = 170 N directed at θ = 35.0 degrees below the horizontal (Figure 1) . The magnitude of the kinetic frictional force between the carpet and the chair is Fk = 108 N . What is the magnitude of the normal force FN acting on the chair? I know you just have to plug the numbers into the equation: N=mg+Fsinθ but in the solution manual they plug in the angle θ as +35 (which gives you a positive Fy component, which I think is wrong) instead of negative (i.e., θ=-35) which I thought was correct since it is below the horizontal. Can you please clarify why the angle was inputted as positive to get the correct answer? Thank you. (My answer was 441 but the key says 637).