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Two persons start walking on a road that diverge at an angle of $120^{\circ}$. If they walk at the rate of $3$km/h and $2$km/h respectively.

Find the distance between them after $4$hrs.

1. $4\sqrt{19}$ km
2. $5$ km
3. $7$ km
4. $8\sqrt{19}$ km

Ans is option (A)

Using the cosine rule of triangle trigonometry ,

$cosC=\frac{a^{2}+b^{2}-c^{2}}{2ab}$

$\Rightarrow$   $cos120^{\circ}=\frac{64+144-c^{2}}{2\times8\times12}$

$\Rightarrow$  $c^{2}=304$   $\Rightarrow$  $c=4\sqrt{19}km$
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