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 $(\text{use}\pi =\frac{22}{7})$.

Answer 1

Here r = 100 cm and l = 22 cm

We know that,

${\theta }^C=\frac{l}{r}$

$\therefore \theta =\frac{22}{100}={\left(\frac{11}{50}\right)}^C$

Now, ${\left(\frac{11}{50}\right)}^C={(\frac{11}{50}\times \frac{180}{\pi })}^0$

= ${(\frac{11}{50}\times \frac{180\times 7}{22})}^0={\left(\frac{63}{5}\right)}^0$

= ${\left(12\frac{3}{5}\right)}^0={12}^0{(\frac{2}{5}\times 60)}^{\prime }$

= ${12}^0{36}^{\prime }$