WAEC 2016 · Paper 2 · Q8

(a)
Forces $(40\text{ N}, 045^\circ)$ and $(Q\text{ N}, 135^\circ)$ act on a body initially at rest. If the magnitude of their resultant is $50\text{ N}$ , find the value of $Q$ .

Worked solution (try it first)

The bearings differ by $135^\circ - 45^\circ = 90^\circ$ , so the forces are at right angles.
By Pythagoras: $50^2 = 40^2 + Q^2$ .
$Q^2 = 2500 - 1600 = 900$ , so $Q = 30\text{ N}$ .