Answer:
31.4 ft
Step-by-step explanation:
The length of an arc is defined as:
[tex]l = \dfrac{\theta}{360\°} \cdot C[/tex]
where:
- [tex]\theta[/tex] = center angle
- [tex]C[/tex] = circumference
Substituting in the definition of circumference, we get:
[tex]l = \dfrac{\theta}{360\°} \cdot 2\pi r[/tex]
Using this formula, we can solve for the given arc length:
[tex]l = \dfrac{150\°}{360\°} \cdot 2\pi (12\text{ ft})[/tex]
[tex]\boxed{l \approx 31.4 \text{ ft}}[/tex]
