Answer:
46°
Step-by-step explanation:
Lets use the formula for arc length (in radian). Then we will convert radians to degrees.
[tex]s=r\theta[/tex]
Where
s is the length of intercepted arc
r is the radius
[tex]\theta[/tex] is the angle in radians
Given,
s = 4
r = 5
We find [tex]\theta[/tex]:
[tex]s=r\theta\\4 = 5\theta\\\theta =\frac{4}{5}=0.8[/tex]
So, central angle = 0.8 radians
To convert from radians to degrees, we use the conversions ratio shown below:
[tex]\pi Radians = 180Degrees[/tex]
So,
[tex]0.8Radians*\frac{180Degrees}{\pi Radians}=\frac{0.8*180}{\pi}=45.84[/tex]
To the nearest degree, we round up to 46°
