Answer:
Given that: AB = 12 ft.
From the given figure we have;
diameter = AB = 12 ft.
[tex]\text{radius} = \frac{diameter}{2} =\frac{12}{2} = 6[/tex] ft.
Supplementary angles states that the two adjacent angles are sum up to 180 degree.
[tex]\angle APC[/tex] and [tex]60^{\circ}[/tex] are supplementary angles.
by definition of supplementary angles;
[tex]\angle APC +60^{\circ} = 180^{\circ}[/tex]
Subtract [tex]60^{\circ}[/tex] from both sides we get;
[tex]\angle APC = 120^{\circ}[/tex]
To find the length of arc AC;
Formula for length(L) of arc is;
[tex]L = 2\pi r \cdot \frac{\theta}{360^{\circ}}[/tex]
[tex]\theta= \angle APC =120^{\circ}[/tex]
substitute the given values; we have;
[tex]L = 2 \pi (6) \cdot \frac{120}{360} = 2 \pi (6) \cdot \frac{1}{3}= 2 \pi (2) = 4 \pi[/tex] ft
Therefore, length of arc AC is, [tex]4 \pi[/tex] ft
