A circle's center is at $(8, 1)$ $(8 ,1 )$ and it passes through $(2, 5)$ $(2 ,5 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

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A circle's center is at $(8, 1)$ $(8 ,1 )$ and it passes through $(2, 5)$ $(2 ,5 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

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Answer 1 · 2018-04-18T06:31:17

$Arc Length s = r \cdot θ = 1.2 π = 3.77 units$ $color(indigo)("Arc Length " s = r * theta = 1.2 pi = 3.77 " units"$

Explanation:

![http://www.1728.org/http://radians.htm](https://useruploads.socratic.org/DXaqqwRrQOSGOu4GMsPq_arc%20length.jpg)

Given : $centre (8,1), Point on circumference (2,5), θ = \frac{π}{6}$ $"centre (8,1), Point on circumference (2,5) ", theta = pi/6$

$Radius r = ¯ ¯¯¯¯ ¯ O A = \sqrt{{(8 - 2)}^{2} + {(1 - 5)}^{2}}$ $" Radius " r = bar (OA) = sqrt ((8-2)^2 + (1-5)^2)$

$r = \sqrt{6^{2} + 4^{2}} = \sqrt{52} = 7.2$ $r = sqrt(6^2 + 4^2) = sqrt 52 = 7.2$

$Arc Length s = r \cdot θ = 7.2 \cdot (\frac{π}{6}) = 1.2 π = 3.77 units$ $color(indigo)("Arc Length " s = r * theta = 7.2 * (pi/6) = 1.2 pi = 3.77 " units"$

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A circle's center is at $(8, 1)$ $(8 ,1 )$ and it passes through $(2, 5)$ $(2 ,5 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

1 Answer

Explanation:

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A circle's center is at $(8, 1)$ $(8 ,1 )$ and it passes through $(2, 5)$ $(2 ,5 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?