Find the degree measure of the angle subtended at the center of a circle of radius \(100\) cm by an arc of length \(22\) cm. \((\text{Use } \pi=\frac{22}{7})\)
Solution:
We know:
\[ s=r\theta \]
Given:
\[ s=22 \text{ cm} \]
\[ r=100 \text{ cm} \]
Using,
\[ \theta=\frac{s}{r} \]
\[ \theta=\frac{22}{100} \]
\[ \theta=\frac{11}{50} \text{ radians} \]
Convert radians into degrees:
\[ \theta=\frac{11}{50}\times\frac{180}{\pi} \]
Using,
\[ \pi=\frac{22}{7} \]
\[ \theta=\frac{11}{50}\times\frac{180\times7}{22} \]
\[ \theta=\frac{1260}{100} \]
\[ \theta=12.6^\circ \]
Therefore, the required angle is:
\[ \boxed{12.6^\circ} \]