SOLUTION: In circle A, the sector PAC is to be filled with blue flowers while the rest of the bed shown in the figure is to be yellow. If radius PA = 8 ft and measure angle PAC = 30 , what

Question 631112: In circle A, the sector PAC is to be filled with blue flowers while the rest of the bed shown in the figure is to be yellow. If radius PA = 8 ft and measure angle PAC = 30 , what is the measure of arc PC ?
(1)3/4 pi
(2)4/3 pi
(3)30 degrees
(4)42 degrees
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The name of a circle is the name of its center. So the center of circle A is the point A. This makes angle PAC a central angle. This is important because we will be using the following proportion which connects central angles and the their related arcs:

           
part       Central Angle      length of arc
-----  =   -------------  =  ----------------
whole          360

Putting the given angle and radius we get:

The left side reduces to:

Cross-multiplying we get:

Dividing by 12:

which reduces to:

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