A circle's center is at $(3, 3)$ $(3 ,3 )$ and it passes through $(4, 5)$ $(4 ,5 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

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Answer 1 · 2016-11-05T09:42:14

$s = π \frac{\sqrt{10}}{6}$ $s=pisqrt10/6$

the arc length of a circle is

$s = r θ$ $s=rtheta$

where $r$ $r$ is the radius, and $θ$ $theta$ the angle in radians subtended at the centre.

radius $r = \sqrt{{(4 - 3)}^{2} + {(5 - 2)}^{2}}$ $r=sqrt((4-3)^2+(5-2)^2)$

$r = \sqrt{1^{2} + 3^{2}} = \sqrt{10}$ $r=sqrt(1^2+3^2)=sqrt10$

$:.s=rtheta=sqrt10xxpi/6$

$s=pisqrt10/6$

A circle's center is at (3 ,3 )(3,3)(3 ,3 ) and it passes through (4 ,5 )(4,5)(4 ,5 ). What is the length of an arc covering ( pi ) /6 π6( pi ) /6 radians on the circle?