A60 newton force is directed in a southwest direction. what are the magnitudes of the force components in the south and west directions?

Hello
This question is to be tackled using vectors. When we look at the Southwest direction, we know it lies exactly between the South and West directions, producing an angle of 45 degrees. When we take sin(45) and multiply it by the original force, we obtain the component towards West; that is:
60 * sin (45) = 42.4 Newtons
And cos(45) gives us the force towards the South direction; that is:
60 * cos(45) = 42.4 Newtons
This can also be checked by using the formula of the magnitude of a vector and squaring 42.4, adding it to the square of 42.4 and then taking the square root of the answer.
sqrt(42.4^2 + 42.4^2) = sqrt(3600) = 60