Two concurrent coplanar forces of magnitude 4 N and 9 N act on a particle. The angle between the two forces is 40 degrees. Find the magnitude of their resultant.

Place the two forces tail to tail with 40 degrees between them. In the triangle of forces the included angle is $180^{\circ}-40^{\circ}=140^{\circ}$, so by the cosine rule

$R^{2}=4^{2}+9^{2}-2(4)(9)\cos 140^{\circ}=16+81+72\cos 40^{\circ}$

$=97+72(0,766044)=97+55,155=152,155$

$R=\sqrt{152,155}=12,3$ N.

The same answer comes from components: $R_{x}=9+4\cos 40^{\circ}=12,064$ and $R_{y}=4\sin 40^{\circ}=2,571$, giving $R=\sqrt{12,064^{2}+2,571^{2}}=12,3$ N.