waecmaths question:
An arc of a circle of radius 7.5cm is 7.5cm long. Find , correct to the nearest degree , the angle which are the arc subtends at the centre of the circle [Take$\pi =\tfrac{22}{7}$]
Option A:
29o
Option B:
57o
Option C:
65o
Option D:
115o
waecmaths solution:
$\begin{align} & l=\frac{\theta }{{{360}^{\circ }}}\times 2\pi r \\ & \text{Given} \\ & \text{length of the arc}=7.5cm \\ & radius=r=7.5cm \\ & 7.5=\frac{\theta }{{{360}^{\circ }}}\times 2\times \frac{22}{7}\times 7.5 \\ & \theta =\frac{7\times {{360}^{\circ }}}{22}\approx {{57}^{\circ }}\text{(to the nearest degree)} \\\end{align}$
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