A circle's center is at $(7, 4)$ $(7 ,4 )$ and it passes through $(8, 2)$ $(8 ,2 )$ . 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 $(7, 4)$ $(7 ,4 )$ and it passes through $(8, 2)$ $(8 ,2 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

1 Answer

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Answer 1 · 2016-11-05T21:56:58

$\sqrt[2]{5} \frac{π}{6}$ $root2(5)pi/6$

Explanation:

The radius is $A P = \sqrt[2]{{(7 - 8)}^{2} + {(4 - 2)}^{2}} = \sqrt[2]{5}$ $AP=root2((7-8)^2+(4-2)^2)=root2(5)$

As the by definition an angle in radiants is exactly the ratio between the arc and the radius of the circumference where that arc is determined by that angle itself, we $\frac{π}{6} =$ $pi/6=$ ("circular arc") $/ R$ $/R$ .
As a result the arc length is "circular arc" $= R \cdot \frac{π}{6}$ $=R*pi/6$

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A circle's center is at $(7, 4)$ $(7 ,4 )$ and it passes through $(8, 2)$ $(8 ,2 )$ . 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 $(7, 4)$ $(7 ,4 )$ and it passes through $(8, 2)$ $(8 ,2 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?