Question

URGENT !! And pls answer in fraction form

The circle below has center O, and its radius is 3 ft. Given that m ZAOB = 30°, find the length of the major arc ACB.
Give an exact answer in terms of , and be sure to include the correct unit in your answer.

Answer 1

`(11\pi)/(2 ) \: ft`

Explanation:

Given:

∠AOB = 30° (it is a central angle, which is equal to the arc on which it rests on)

r (radius) = 3 ft

Find: arc ACB - ?

If arc AB is 30°, then arc ACB is (remember, that a full circle forms an angle of 360°)

`360° - 30° = 330°`

Now, we can find the length of the arc ACB:

`l = (2\pi * r * \alpha )/(360°) = (2\pi * 3 * 330°)/(360°) = (11\pi)/(2) \: ft`