Question

An arc of length 15 cm subtends an angle of ${45}^{\circ }$ at the centre of a circle. Find in terms of $\pi$, the radius of the circle.

Answer 1

We know that the arc length $l$ of a sector of an angle $\theta$ in a circle of radius $r$ is

$l=\frac{\theta }{{360}^o}\times 2\pi r$

$\Rightarrow 15=\frac{45}{360}\times 2\pi r$

$\therefore r=\frac{60}{\pi }cm$