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Find the length of each arc. leave in terms of pi and simplify.

Find the length of each arc. leave in terms of pi and simplify.-example-1

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1st arc: 15π cm (18cm radius, 150° angle). 2nd arc: 14π/3 m (20m radius, 210° angle). Both lengths proportional to their central angles.

The lengths of the arcs can be found using the formula:

`s = r * θ`

where:

* `s` is the arc length

* `r` is the radius of the circle

* `θ` is the central angle of the arc, in radians

In the first arc, the central angle is 150 degrees. Converting this to radians, we get:

`θ = 150° * π/180° = 5π/6`

Substituting the values of `r` (18 cm) and `θ` into the formula, we get the length of the first arc:

`s₁ = 18 cm * 5π/6 = 15π cm`

In the second arc, the central angle is 210 degrees. Converting this to radians, we get:

`θ = 210° * π/180° = 7π/6`

Substituting the values of `r` (20 m) and `θ` into the formula, we get the length of the second arc:

`s₂ = 20 m * 7π/6 = 14π/3 m`

Therefore, the lengths of the arcs are:

* First arc: 15π cm

* Second arc: 14π/3 m

User Igalarzab
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