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I have the question "Resolve the forces acting on the following objects into their vertical and horizontal components and thus find the vertical and horizontal components of their resultant force.

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The solutions say that the answer should be:

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And I know that I have to use trigonometry but I am not sure how the answer is achieved.

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Extend the vertical line in the top figure might help.

The vertical upward force can be computed by

$$3-4 \cos(180 ^\circ-125^\circ)$$

The horizontal force towards the left can be computed by

$$4-4 \sin(180^\circ - 125 ^\circ)$$