Question #5de41

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Answer 1 · 2015-06-21T13:41:59

The answer is #sqrt(37)"N"#.

Because the angle between the two forces is not #90^@#, you cannot apply Pythagoras' Theorem to determine the magnitue of the resultant.

However, you can apply the Parallelogram of force to determine the magnitude of the resultant.

![ ocw.metu.edu.tr )

The formula you're going to use looks like this

#F^2 = F_1^2 + F_2^2 + 2F_1F_2cos(theta)#, where

#theta# - the angle between the two forces, in your case equal to #120^@#.

This means that you have

#F^2 = 4^2 + 7^2 + cancel(2) * 4 * 7 * (-1/cancel(2))#

#F^2 = 16 + 49 - 28 = 37 => F = color(green)(sqrt(37)"N")#