JAMB 2015 · UTME · Q4

Sine & cosine rules

A force of 5 units acts on a particle in the direction due east and another force of 4 units acts on the particle in the direction north-east. The resultant of the two forces is

Worked solution (try it first)

East and north-east are $45^\circ$ apart.
In the triangle of forces (5 east, then 4 north-east), the angle between them is $180^\circ - 45^\circ = 135^\circ$ .
Cosine rule for the resultant: $R^2 = 5^2 + 4^2 - 2(5)(4)\cos135^\circ$ .
$\cos135^\circ = -\frac{\sqrt2}{2}$ , so the last term is $+40 \times \frac{\sqrt2}{2} = +20\sqrt2$ and $R^2 = 41 + 20\sqrt2$ .
So $R = \sqrt{41 + 20\sqrt2}$ units, option C.

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