Given:
Given that O is the center of the circle.
The radius of the circle is 3 m.
The measure of ∠AOB is 30°
We need to determine the length of the major arc ACB
Measure of major ∠AOB:
The measure of major angle AOB can be determined by subtracting 360° and 30°
Thus, we have;
[tex]Major \ \angle AOB=360-30[/tex]
[tex]Major \ \angle AOB=330^{\circ}[/tex]
Thus, the measure of major angle is 330°
Length of the major arc ACB:
The length of the major arc ACB can be determined using the formula,
[tex]m \widehat{ACB}=(\frac{\theta}{360})2 \pi r[/tex]
Substituting r = 3 and [tex]\theta=330[/tex], we get;
[tex]m \widehat{ACB}=(\frac{330}{360})2 \pi (3)[/tex]
[tex]m \widehat{ACB}=\frac{1980}{360}\pi[/tex]
[tex]m \widehat{ACB}=5.5 \pi[/tex]
Thus, the length of the major arc ACB is 5.5π m
