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The perimeter of sector $OAB$ of a circle with centre $O$ and radius $5.6$ cm, is $15.6$ cm. Find length of the arc $AB$. Also find the value of $\theta$.
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Sol. Length of the arc $AB = \text{Perimeter of sector} - 2r$
$= 15.6 - 11.2$
$= 4.4$ cm (I) (1 Mark)
$\therefore 4.4 = \frac{\theta}{360} \times 2 \times \frac{22}{7} \times 5.6$ (II) (1 Mark)
$\Rightarrow \theta = 45^\circ$ (III) (1 Mark)
$= 15.6 - 11.2$
$= 4.4$ cm (I) (1 Mark)
$\therefore 4.4 = \frac{\theta}{360} \times 2 \times \frac{22}{7} \times 5.6$ (II) (1 Mark)
$\Rightarrow \theta = 45^\circ$ (III) (1 Mark)