# Resolve the 250 N force into components

Resolve the 250 N force into components acting along the u and v axes and determine the magnitudes of these components.

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

#### Solution:

We will first draw the components along the u and v axes like so:

The angles were found using  alternate interior angles theorem, corresponding angles theorem and consecutive angles theorem.

We can now draw the components tail to tail as follows:

We can now use sine law to figure out the forces.

$\dfrac{250}{\sin120^0}\,=\,\dfrac{F_u}{\sin40^0}$

(solve for $F_u$)

$F_u\,=\,185.5$ N

$\dfrac{250}{\sin120^0}\,=\,\dfrac{F_v}{\sin20^0}$

(solve for $F_v$)

$F_v\,=\,98.7$ N

$F_u\,=\,185.5$ N
$F_v\,=\,98.7$ N