Given:
The central angle = [tex]\theta[/tex]
Radius of the circle = 4 ft
Intercepted arc length = 50ft
To find:
The value of [tex]\theta [/tex] in radian measure.
Solution:
The formula for arc length is
[tex]s=r\theta[/tex]
where, r is radius and [tex]\theta [/tex] is the central angle in radians.
Putting s=50 and r=4, we get
[tex]50=4\theta[/tex]
Divide both sides by 4.
[tex]\dfrac{50}{4}=\theta[/tex]
[tex]12.5=\theta[/tex]
Therefore, the value of [tex]\theta [/tex] is 12.5 radians.
