waecmaths question:
A piece of thread of length 21.4cm is used to form a sector of a circle of radius 4.2cm on a piece of cloth. Calculate, correct to the nearest degree, the angle of the sector.[Take $\pi=\tfrac(22/7)]
Option A:
170o
Option B:
177o
Option C:
182o
Option D:
192o
waecmaths solution:
$\begin{align} & \text{Perimeter of the sector}=\left[ \frac{\theta }{{{360}^{\circ }}}\times 2\pi r \right]+2r \\ & 21.4cm=\left[ \frac{\theta }{360{}^\circ }\times 2\times \frac{22}{7}\times 4.2cm \right]+2(4.2cm) \\ & 21.4cm-8.4cm=\frac{\theta }{360{}^\circ }\times 2\times \frac{22}{7}\times 4.2cm \\ & 13cm=\frac{11cm\times \theta }{150{}^\circ } \\ & \theta =\frac{13cm\times 150{}^\circ }{11cm}=177.27 \\ & \theta \approx 177{}^\circ \text{ to the nearest degree}\text{.} \\\end{align}$
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