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Find the measurement of an arc on a circle that has a radius of 6ft and an inner...

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jasminehems | Student, Undergraduate | Honors

Posted April 27, 2013 at 7:03 AM via web

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Find the measurement of an arc on a circle that has a radius of 6ft and an inner measurement angle of 36 degrees.

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jasminehems | Student, Undergraduate | Honors

Posted April 27, 2013 at 7:14 AM (Answer #1)

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The formula to find the legnth of an arc on a circle is a proportion:

`((mArc)/(perimeter)) * (( angle)/(360))` 

Firstly we need to find the perimeter of our circle, which we can find with the formula:

`P = pi r^2` 

So lets plug in the numbers.

`P= pi 6^2` ``

`P~~113.1`

Now that we know our perimeter, we can plug in all the numbers we have into our original formula.

 `((mArc)/(113.1))*((36)/(360))`

Now cross multiply and solve for x.

`360x = 4071.6` 

`(360x)/(360) = (4071.6)/(360)` ``

`mArc = 11.31ft`

 

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jasminehems | Student, Undergraduate | Honors

Posted April 27, 2013 at 7:17 AM (Answer #2)

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The formula to find the legnth of an arc on a circle is a proportion:

 

Firstly we need to find the perimeter of our circle, which we can find with the formula:

 

So lets plug in the numbers.

 

Now that we know our perimeter, we can plug in all the numbers we have into our original formula.

 

Now cross multiply and solve for x.

 

 

 

Should be `P= 2 pi r`

therefore, `P~~37.7`

and then the final answer should be `mArc ~~ 3.77 ft`

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rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted April 27, 2013 at 7:23 AM (Answer #3)

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We know that the length of arc `L=rtheta` .

where `r`  is the radius of the circle and `theta`  is the angle in radian subtended by this arc at the centre of the circle.

         Given  `r=6`  ft. and   `theta=36` degree.

We know that to change `theta`  in degree to radian we multiply the degree value by `pi/180` .

So,   `theta`  (in radian)=`36pi/180` =`pi/5` .

Now length of arc  `L=6pi/5` .

Taking  `pi=22/7` ,

we get    `L=6(22/7)(1/5)=3.771`  ft. Answer.

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