Question

If the measurement of a central angle is 5pi/6, find the length of its intercepted arc in a circle with a radius of 15 inches

Answer 1

Arc length = angle / 2pi * pi(d)

= 5pi/6 / 2pi * pi*30

= 25pi/2 or approximately 39.3inches

Answer 2

The exact value of the arc length is
`12.5\pi \ inches`

or

The approximately value of the arc length is
`39.27\ inches`

Explanation:

we know that

By proportion

`(central\ angle)/(2\pi)=(arc\ length)/(2\pi r)`

in this problem we have

`central\ angle=(5\pi)/(6)`

`r=15\ inches`

substitute the values

`((5\pi)/(6))/(2\pi)=(arc\ length)/(2\pi (15))\\ \\(5\pi)/(12\pi) =(arc\ length)/(30\pi) \\ \\ arc\ length=30\pi *(5/12)\\ \\arc\ length=12.5\pi \ inches`

`arc\ length=39.27\ inches`