A circle's center is at $(8, 3)$ $(8 ,3 )$ 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 $(8, 3)$ $(8 ,3 )$ 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 · 2016-04-15T10:26:28

Length of the arc is $3.312$ $3.312$ units.

Explanation:

As the circle's center is at $(8, 3)$ $(8,3)$ and it passes through $(2, 5)$ $(2,5)$ , its radius is the distance between two points i.e.

$\sqrt{{(2 - 8)}^{2} + {(5 - 3)}^{2}} = \sqrt{36 + 4} = \sqrt{40} = 6.325$ $sqrt((2-8)^2+(5-3)^2)=sqrt(36+4)=sqrt40=6.325$

Hence length of the arc covering angle $\frac{π}{6}$ $pi/6$ is given by $r \times θ$ $rxxtheta$ , where $r$ $r$ is radius and $θ$ $theta$ angle in radians.

Hence, length of the arc is $6.325 \times \frac{π}{6} = \frac{6.325 \times 3.1416}{6} = 3.312$ $6.325xxpi/6=(6.325xx3.1416)/6=3.312$

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A circle's center is at $(8, 3)$ $(8 ,3 )$ 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 (8,3)(8 ,3 ) and it passes through (2,5)(2 ,5 ). What is the length of an arc covering π6( pi ) /6 radians on the circle?

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A circle's center is at $(8, 3)$ $(8 ,3 )$ 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?