The chord ST of a circle is equal to the radius r of the circle. Find the length of arc ST
A.
\(\frac{\pi r}{3}\)
B.
\(\frac{\pi r}{2}\)
C.
\(\frac{\pi r}{12}\)
D.
\(\frac{\pi r}{6}\)
Correct answer is A
\(\frac{ \frac{r}{2}}{r}\) Sin \(\theta\) = \(\frac{1}{2}\)
\(\theta\) = sin\(^{-1}\) (\(\frac{1}{2}\)) = 30\(^o\) = 60\(^o\)
Length of arc (minor)
ST = \(\frac{\theta}{360}\) x 2\(\pi r\)
\(\frac{60}{360} \times 2 \pi \times r = \frac{\pi}{3}\)