Question

Find the degree measure of the angle subtended at the centre of a circle of radius $100$ cm by an arc of length $22$ cm. $(Use\pi =\frac{22}{7})$

Answer 1

We know that in a circle of radius $r$ unit, if an arc of length $l$ unit
subtends an angle $\theta$ radian at the centre, then $\theta =\frac{l}{r}$
Therefore, for $r=100$ cm, $l=22$ cm, we have
$\theta =\frac{22}{100}radian=\frac{180}{\pi }\times \frac{22}{100}degree=\frac{180\times 7\times 22}{22\times 100}$ degree
$=\frac{126}{10}degree=12\frac{3}{5}degree={12}^{\circ }{36}^{\prime }$ $,[\because 1^{\circ }={60}^{\prime }]$