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  4. Two forces of magnitude 8 N and 15 N respectively act at a point. If the resultant force is 17 N, the angle between the forces has to be

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Q. Two forces of magnitude $8\, N$ and $15\, N$ respectively act at a point. If the resultant force is $17\, N$, the angle between the forces has to be

Motion in a Plane

Solution:

$R=\sqrt{A^{2}+B^{2}+2 A B \cos \theta}$
$A=8, B=15, R=17$
$17^{2}=8^{2}+15^{2}+2 \times 8 \times 15 \times \cos \theta$
$289=64+225+240 \cos \theta$
$\Rightarrow 289=289+24 \cos \theta$
$24 \cos \theta=0$
$\cos \theta=0 \Rightarrow \theta=90^{\circ}$