Question

8. Find the length of AC

Express your answer in terms of .
60°
A
B
P
AB = 12 ft
a
16 ft

Answer 1

AC = 4π ft

Explanation:

The length of arc AC is calculated as

AC = circumference of circle × fraction of circle

∠ APC = 180° - 60° = 120° ( adjacent angles on a straight line sum to 180° )

diameter AB = 12 , so radius r = 12 ÷ 2 = 6 , then

AC = 2πr ×
`(120)/(360)`

= 2π × 6 ×
`(1)/(3)`

= 12π ×
`(1)/(3)`

= 4π ft