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Consider circle C with radius 5 cm and a central angle measure of 60°. Circle C is shown. Line segments R C and S C are radii with length of 5 centimeters. Angle R C S is 60 degrees. What fraction of the whole circle is arc RS? What is the approximate circumference of the circle? cm What is the approximate length of arc RS? cm

Respuesta :

Answer:

1. 1/6

2. 31.4

3. 5.2

Step-by-step explanation:

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

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