Question

1. for a circle with a radius of 5 meters, what is the length of an arc that subtends a 30° angle?

a. 10π meters
b. 5π meters
c. \\(\frac{5π}{6}\\) meters
d. \\(\frac{10π}{3}\\) meters

Explanation:

Step1: Convert degrees to radians

$30^\circ = 30 \times \frac{\pi}{180} = \frac{\pi}{6}$ radians

Step2: Calculate arc length

Arc length formula: $s = r\theta$, where $r=5$, $\theta=\frac{\pi}{6}$.
$s = 5 \times \frac{\pi}{6} = \frac{5\pi}{6}$

Answer:

c. $\frac{5\pi}{6}$ meters