NECO 2023 · Paper 1 · Q38

Find the magnitude of the resultant of two forces of 5 N and 4 N acting at a point if the angle between them is $60^\circ$ .

Worked solution (try it first)

For two forces $P$ and $Q$ at an angle $\theta$ , the resultant is given by $R^2 = P^2 + Q^2 + 2PQ\cos\theta$ .
$R^2 = 25 + 16 + 2(5)(4)\cos60^\circ$ , and $\cos60^\circ = \frac12$ , so $R^2 = 41 + 20 = 61$ .
So $R = \sqrt{61} \approx 7.8$ N, option D.