Translational eq. question

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lets say you have a box you give it 100N in the West direction and 200N in the North direction. What angle and force is required to keep the box in translation equlibrium?

I was able to solve this the q with common sense using the answer choices but how would i do this mathematically?? i remember doing this in high school, too bad i didnt learn anything then

 

[ilovemcat]

In object in translational equilibrium has a net force of 0 N both in the Y-direction and X-direction. Therefore, to to balance the other two forces, you need a force applied 200 N south and 100N east. Use pythagerean theorem to figure out the magnitude of this force.

= sqrt(200^2 + 100^2)
= 223 N @ 27 degrees East of South

To figure out the angle, use your trig functions: Cos(theta) = Adj / Hyp = 200 N / 223 N = 0.89 which is approximately an angle of 27 degrees with respect to the vertical.