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an arc of a circle measures 60 degrees to radius in 80 cm what is the length of the arc​

Sagot :

UK2019idn

✏️ARC LENGTH

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Problem: The arc of a circle measures 60 degrees and it's radius is 80 cm. What is the length of the arc?

Solution: Find the length of the arc in which it is the product of the ratio of the angle subtended to it at 360 degrees, and the circle's circumference.

[tex] \begin{aligned}& \bold{ \color{lightblue}Formula: } \\ & \boxed{ \ell = \frac{ \theta}{360 \degree} \cdot2\pi r } \end{aligned}[/tex]

- The diameter of the circle is twice its radius, thus we can say that the circumference of the circle is the product of its diameter and pi.

  • [tex]\begin{aligned}{\ell = \frac{60 \degree}{360 \degree} \cdot2\pi(80cm) } \end{aligned}[/tex]

  • [tex]\begin{aligned}{\ell = \frac{1}{6} \cdot\pi(160cm) } \end{aligned}[/tex]

  • [tex]\begin{aligned}{\ell = \frac{\pi(160cm) }{6}} \end{aligned}[/tex]

  • [tex] \ell = \pi(26.67cm)[/tex]

- Let 3.14 be the approximate value of pi.

  • [tex] \ell ≈ (3.14)(26.67cm)[/tex]

  • [tex] \ell ≈ 83.74cm[/tex]

- Therefore, the length of the arc is:

  • [tex] \large \rm Arc \: Length = \boxed{ \rm \green{ \: 83.74 \: cm \: }}[/tex]

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