Three vectors lie in an xy plane

[0btuse]

Homework Statement

Three vectors A, B, C, each have a magnitude of 46 m and lie in an xy plane. Their directions relative to the positive direction of the x-axis are 28 ˚, 191 ˚, and 313 ˚.

What are the magnitude and the angle of A-B+C with right-arrow in the range of (-180°, 180°)?

Homework Equations

The Attempt at a Solution

Nx = 46cos(28)-46cos(191)+46cos(313)= 117.15
Ny = 46sin(28)-46sin(191)+46sin(313) = -3.26

N= sqrt((117.15^2)+(-3.26)^2)
N = 117.11

For the angle i have tan^-1 (-3.26/117.15) = -1.60°

the online homework is accepting my answer for the angle as being correct, however I'm not as fortunate with the magnitude.

 

[TSny]

Your method is correct. I get a slightly different answer when I calculate the magnitude. It differs in the fourth digit. I don't know how accurate your answer needs to be.

 

[0btuse]

i suppose i'll have to take the hit on the assignment because no matter how I round it's not accepting my answer. I've tried adding additional sigfigs to no avail. thank you for your response. it's been driving me crazy.

 

[TSny]

I think your answer is correct. Maybe an error in the grading system.

Edit: It looks like when you calculated the magnitude you might have calculated it as $\sqrt{117.15^2 - (3.26)^2}$ rather than $\sqrt{117.15^2 + (-3.26)^2}$

 

[0btuse]

i emailed the professor and it appears there was an error in that it was forcing significant digits.
the answer was 120.
thank you again. just thought i'd update for anyone else that may drive themselves nuts over this in the future.

 

[TSny]

OK. That makes sense. Only two significant figures are given for the magnitudes of the vectors. It's sometimes hard to know how grading systems are handling significant figures.