The length of an arc is the distance between the endpoints of the arc.
The central angle is: [tex]\mathbf{4.75\ rad}[/tex] or [tex]\mathbf{272.16^o}[/tex]
The given parameters are:
[tex]\mathbf{l = 19yd}[/tex] --- length of the arc
[tex]\mathbf{r = 4}[/tex] -- radius of the circle
The length of an arc is calculated as:
[tex]\mathbf{l =r\theta}[/tex]
Divide both sides by r
[tex]\mathbf{\theta = \frac lr}[/tex]
Substitute known values
[tex]\mathbf{\theta = \frac{19}4}[/tex]
[tex]\mathbf{\theta = 4.75\ radians}[/tex]
Convert to degrees as follows:
[tex]\mathbf{\theta = 4.75 \times \frac{180}{\pi}}[/tex]
[tex]\mathbf{\theta = 4.75 \times \frac{180}{3.142}}[/tex]
[tex]\mathbf{\theta = 272.16^o}[/tex]
Hence, the central angle is: [tex]\mathbf{4.75\ rad}[/tex] or [tex]\mathbf{272.16^o}[/tex]
Read more about length of arcs at:
https://brainly.com/question/15832640
