Question

Find the angle subtended at the centre of a circle of radius 'a' by an arc of length $\left(\frac{a\pi }{4}\right)cm$

Answer 1

Angle subtended by circumference ($2\pi a$) at the centre $={360}^o$

$\Rightarrow$ Angle subtended by unit arc length $=\frac{{360}^o}{2\pi a}$

$\therefore$ Angle subtended by an arc of length $\frac{a\pi }{4}$ $=\frac{{360}^o}{2\pi a}\times \frac{a\pi }{4}={45}^o$