Question

Find the length of arc AC. Express your answer in terms of pi.

Answer 1

Length of Arc = Ф/360 * 2πr

l = 120/360 * 2π(6)

l = 1/3 * 12π

l = 4π

In short, Your Answer would be: 4π Feet

Hope this helps!

Answer 2

Given that: AB = 12 ft.

From the given figure we have;

diameter = AB = 12 ft.

`\text{radius} = (diameter)/(2) =(12)/(2) = 6` ft.

Supplementary angles states that the two adjacent angles are sum up to 180 degree.

`\angle APC` and
`60^(\circ)` are supplementary angles.

by definition of supplementary angles;

`\angle APC +60^(\circ) = 180^(\circ)`

Subtract
`60^(\circ)` from both sides we get;

`\angle APC = 120^(\circ)`

To find the length of arc AC;

Formula for length(L) of arc is;

`L = 2\pi r \cdot (\theta)/(360^(\circ))`

`\theta= \angle APC =120^(\circ)`

substitute the given values; we have;

`L = 2 \pi (6) \cdot (120)/(360) = 2 \pi (6) \cdot (1)/(3)= 2 \pi (2) = 4 \pi` ft

Therefore, length of arc AC is,
`4 \pi` ft