Question

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

Answer 1

Step 1: Simplify for angle $\theta$
Radius of circle, $r=100\text{cm}$
Length of arc, $l=22\text{cm}$
Using formula $\theta =\frac{l}{r}\Rightarrow \theta =\frac{22}{100}$ radian

Step 2: Convert radian into degree.
${180}^{\circ }=\pi$ radian
$\therefore \theta =\frac{22}{100}\times \frac{180}{\pi }$ degree = $\frac{180\times 7\times 22}{22\times 100}$ degree $\{\because \pi =\frac{22}{7}\}$
= $\frac{126}{10}$ degree $={12}^{\circ }36\text{'}\{\because 1^{\circ }={60}^{\prime }\}$
The required angle is ${12}^{\circ }36\text{'}$.