What you need to know is basically that the adjacent leg in a right triangle is hypotenuse times cosine of the angle and that the opposite leg is hypotenuse times sine of the angle. - It's as easy as that.

This means, for example, that the length of the orthogonal projection of F onto the xy-plane has length . You get the length of the projections of F onto the x- and y-axis by multiplying that with , and , respectively.