# how to compute the resultant force of an angle given?

gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

Your question is not very clear.

If the magnitude of a force is given and that the force is acting at an angle to the traditional axes (x & y, i.e. horizontal and vertical), we resolve the force into two components, each acting along the traditional axes. This is done using trigonometry.

If the angle with respect to x-axis (or horizontal) is given, the horizontal component is the cosine of force (i.e., Fcos`Theta` ) and the vertical component is sine of the force (i.e., Fsin`theta` ).

If you are given two forces and the angle between them, then the resultant force can be calculated using parallelogram law. Suppose the two forces are A and B and the angle between them is `theta` , then the resultant force (F) is given as

`F = sqrt(A^2 + B^2 + 2AB cos theta)`

and the direction of the resultant force is given by

`alpha = tan^(-1) [(Bsin theta)/(A+Bcos theta)]`

hope this helps