If the resultant force of the two tugboats is 3 kN, directed along the x positive axis, determine the required magnitude of force F_B and its direction θ.

#### Solution:

Let us first draw the vector components like so.

Now let’s draw the vectors tail to tail as follows.

From this, we can figure out FB by using the law of cosines. (Forgot the law of cosines?)

(F_B)^2=2^2+3^2-2(2)(3)\cos 30^0

F_B=\sqrt{2^2+3^2-2(2)(3)\cos 30^0}

F_B=1.615 kN

To figure out θ we can use the law of sines. (Forgot the law of sines?)

\dfrac{\sin \theta}{2}=\dfrac{\sin 30^0}{1.615}
\theta=38.3^0