Answer:
[tex]\sf \theta=\dfrac34 \ radians=42.97 \textdegree \ (nearest \ hundredth)[/tex]
Step-by-step explanation:
Formulae
[tex]\sf radius (r)=\dfrac12 d[/tex]
(where d is the diameter of a circle)
[tex]\sf arc \ length =r\theta[/tex]
(where r is the radius and [tex]\theta[/tex] is measured in radians)
Calculation
Given:
Substituting these values into the formula for arc length:
[tex]\implies \sf 3 =4\theta[/tex]
[tex]\implies \sf \theta=\dfrac34 \ radians[/tex]
To convert radians to degrees use
[tex]\sf 1 \ rad \cdot \dfrac{180\texrdegree}{\pi}[/tex]
[tex]\implies \sf \dfrac34 \cdot \dfrac{180\texrdegree}{\pi}=42.97183463...\textdegree[/tex]
Now
[tex]\\ \rm\rightarrowtail \theta=\dfrac{l}{r}[/tex]
[tex]\\ \rm\rightarrowtail l=r\theta[/tex]
[tex]\\ \rm\rightarrowtail 3=4\theta[/tex]
[tex]\\ \rm\rightarrowtail \theta=\dfrac{3}{4}^c[/tex]
