Answer:
Option 4th is correct
76.39 degree
Step-by-step explanation:
The arc length(l) is given by:
[tex]l =r \theta[/tex] .....[1]
where, r is the radius of the circle and [tex]\theta[/tex] is the central angle in radian
As per the statement:
An arc of length 12 meters is formed by a central angle A on a circle of radius 9
⇒l = 12 meters and r = 9 meter
substitute the given values in [1] we have;
[tex]12 = 9A[/tex]
Divide both sides by 9 we have;
[tex]\frac{12}{9} =A[/tex]
Use conversion:
1 radian = 57.2958 degree
then;
[tex]\frac{12}{9}[/tex] radian = 76.3943998 degree.
⇒[tex]A = 76.39^{\circ}[/tex]
Therefore, the measure of angle A in degree is, 76.39
