Answer:
For this particular problem (with units in mind), the formula for arc length is
Arc length
=
2
π
r
⋅
(
x
360
∘
)
,
Where
x
is the central angle measure and
r
is the radius of the circle.
You don't really have to work too hard to remember this formula. The arc length formula is easy to remember because it is just the circumference of the circle times the central angle over
360
∘
.
Anyway, let's continue with the problem. We are given that the central angle is
60
∘
, and that
r
, our radius, is
9
feet. So, let's plug that into our equation to find the arc length, in feet:
Arc length
=
2
π
r
⋅
(
x
360
∘
)
Arc length
=
2
π
(
9
)
⋅
(
60
∘
360
∘
)
Now, you might be tempted to plug this in your calculator, but let's simplify it a little bit more.
Arc length
=
2
π
(
9
)
⋅
(
60
∘
360
∘
)
Arc length
=
18
π
⋅
(
1
6
)
Arc length
=
3
π
feet
So, if you wanted an exact answer, it would be that the arc length is
3
π
feet
. If you wanted an approximate answer, then you can type
3
times
π
in your calculator to get a value of about
9.425
feet
as you alternative answer.
Explanation: