Question

Find in degrees the angle subtended at the centre of a circle of a diameter 50 cm by an arc of length 11 cm.

Answer 1

Here, r = 25 cm and l = 11 cm.

Let the measure of the required angle be ${\theta }^c$.

Then, ${\theta }^c$ = ${\left(\frac{l}{r}\right)}^c={\left(\frac{11}{25}\right)}^c$

=${(\frac{11}{25}\times \frac{180}{\pi })}^{\circ }[\because {\pi }^c={180}^{\circ }]$

=${(\frac{11}{25}\times \frac{7}{22}\times 180)}^{\circ }$

= ${\left(\frac{126}{5}\right)}^{\circ }={25}^{\circ }12‘$

Hence, the required angle is ${25}^{\circ }12‘$