Two forces have magnitudes $P$ and $Q$ and the acute angle between them is $\theta$ , so their resultant has magnitude $R$ where $R^{2}=P^{2}+Q^{2}+2PQ\cos\theta$ . Two forces of magnitudes 5 N and 8 N act at an angle of $60^{\circ}$ to each other. Find the magnitude of their resultant, in newtons, correct to 3 significant figures.

Model answer

11,4

Also accepted: 11.4, 11,36, 11.36, 11,358, 11.358, sqrt(129), 11,4 N, 11.4 N

Explanation

Substituting $P=5$ , $Q=8$ and $\theta=60^{\circ}$ , with $\cos60^{\circ}=0.5$ :
$R^{2}=5^{2}+8^{2}+2(5)(8)(0.5)=25+64+40=129$ .

So $R=\sqrt{129}=11.358$ , that is $11.4$ N to 3 significant figures.

Derived from ZIMSEC Mathematics 9164/4 Paper 4, November 2011, Q12

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