Respuesta :
You can use formula for circumference of the circle and circumference to arc relation here.
The length of the arc RS is [tex]\dfrac{5\pi}{3}[/tex]circumference of the circle is [tex]10\pi[/tex].
The arc RS is [tex]\dfrac{1}{6}[/tex] fraction of the whole circumference.
Given that:
- The circle C has radius = 5 cm
- The line segments RC and SC are radii of circle C
- The angle RCS = 60 degrees.
The circumference of the circle is calculated as:
[tex]\:\rm Circumference = 2 \pi r = 2 \pi \times 5 = 10\pi[/tex] cm
Since 360 degrees cover whole circle's circumference, thus:
[tex]360^{\circ} \: \text{covers} \: 2\pi r = 10\pi \:\rm cm\\\\1^\circ \: \: \rm covers \: \:\dfrac{\pi}{36}\: \rm cm\\\\or\\\\60^\circ \: \: \rm covers \: \: \dfrac{60\pi}{36} \: cm = \dfrac{5\pi}{3} \: \rm cm[/tex]
Ratio of arc RS and circumference:
[tex]\dfrac{arc\: \: RS}{Circumference} = \dfrac{\dfrac{5\pi}{3}}{10\pi} = \dfrac{1}{6}[/tex]
Thus, the length of the arc RS is [tex]\dfrac{5\pi}{3}[/tex], and the circumference of the circle is [tex]10\pi[/tex]. The arc RS is [tex]\dfrac{1}{6}[/tex] fraction of the whole circumference.
Learn more about arc length here:
https://brainly.com/question/7488987
