Application of vectors in physics

Example: A 35-N weight is suspended by two wires. Find the forces F1 and F2 acting in both wires.
Solution: The force vectors F1 and F2 have magnitudes |F1| and |F2| and components that are measured in Newtons. The resultant force is the sum F1 + F2 and must be equal in magnitude and acting in the opposite (or upward) direction to the weight vector w. It follows from the figure (see Geogebra file) that: F1 = <-|F1| cos 40, |F1| sin 40> and F2 = <|F2| cos 50, |F2| sin 50> Note: You can change the values for the weight by moving the slider w, and the value of the angles is changed by moving the sliders alpha and beta.