Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
The length of the arc which subtends a [tex]\pi/3[/tex] radians angle on a circle with 6 ft radius is given by: Option C: 6.3 feet approximately.
How to find the relation between angle subtended by the arc, the radius and the arc length?
[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]
The superscript 'c' shows angle measured is in radians.
If radius of the circle is of r units, then:
[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]
For this case, we have:
- Radius of the circle = r = 6 ft
- Angle subtended by the considered arc of the circle on its center = [tex]\theta^c = \dfrac{\pi}{3}^c[/tex]
Thus, if we take:
Length of the arc = L feet, then:
[tex]L =r \times \theta = 6 \times \dfrac{\pi}{3} = 2\pi \: \rm ft \approx 6.28 \approx 6.3 \: ft[/tex]
Thus, the length of the arc which subtends a [tex]\pi/3[/tex] radians angle on a circle with 6 ft radius is given by: Option C: 6.3 feet approximately.
Learn more about arc length here:
https://brainly.com/question/12058177
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
