Answer:
2.78 radians or 159.36°
Step-by-step explanation:
Givens:
[tex]r=13in[/tex]
[tex]\theta =?[/tex]
[tex]s=3 ft[/tex]
[tex]s[/tex] refers to the length of the circumference, which is the same distance rolled.
So, to find the angle, we have to use this definition:
[tex]s=\theta r[/tex]; which is the relation between arc, angle and length.
Before, replacing all values, we have to transform 13 inches in feet. We know that 1 feet is 12 inches. So,
[tex]13in\frac{1ft}{12in}=1.08ft[/tex]
Now, we find the angle.
[tex]s=\theta r\\\theta=\frac{3ft}{1.08ft}=2.78 \ rad[/tex]
Therefore, the angle is 2.78 radians.
To have it in degrees, we have to transform.
[tex]\pi \ rad =180\°\\2.78 \ rad \frac{180\°}{\pi rad}=\frac{500.4}{3.14}=159.36\°[/tex]
