Discussion

If arc of circle of radius 30 cm has a length of 19 cm then angle subtended at center of circle is

Answer: D

Arc length and central angle are related by \( s = r\theta \) with \( \theta \) in radians.

\[ \theta = \frac{s}{r} = \frac{19}{30} = 0.6333 \text{ rad} \]

Converting to degrees:

\[ 0.6333 \times \frac{180}{\pi} = 36.28^{\circ} \]

The formula \( s = r\theta \) works only in radians; in degrees it needs the extra factor \( \tfrac{\theta}{360} \times 2\pi r \).

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