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

Let, AB = arc AB = 22 cm

OA = OB = r = 100 cm

Let $\theta$ be the angle subtended by arc AB at centre O.

$\therefore by\theta =\frac{\text{arc}}{\text{radius}}\Rightarrow \theta =\frac{22}{100}\text{radian}\therefore \theta ={(\frac{22}{100}\times \frac{180}{\pi })}^{\circ }[\because 1\text{radian}={\left(\frac{180}{\pi }\right)}^{\circ }]={12.6}^{\circ }={12}^{\circ }{36}^{\prime }[1^{\circ }={60}^{\prime }]\therefore \theta ={12}^{\circ }{36}^{\prime }$