SOLUTION: theta is a central angle in a circle of radius r = 5 mm. Find the length of arc s cut off by theta; = 330°. (Round the answer to two decimal places.) How do you work this problem

Algebra ->  Trigonometry-basics -> SOLUTION: theta is a central angle in a circle of radius r = 5 mm. Find the length of arc s cut off by theta; = 330°. (Round the answer to two decimal places.) How do you work this problem      Log On


   

Question 412206: theta is a central angle in a circle of radius r = 5 mm. Find the length of arc s cut off by theta; = 330°. (Round the answer to two decimal places.) How do you work this problem?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Central angles, their arcs and the areas of the sectors formed are all proportional:
     central angle           arc length           area of sector
  ------------------    =   -------------   =   ------------------
  2pi or 360 degrees        Circumference       area of the circle

For your problem, which references central angles and arc length we will use the first two fractions:
     central angle           arc length
  ------------------    =   -------------
  2pi or 360 degrees        Circumference

Since your central angle is expressed in degrees we will use 360 in the denominator of the first fraction:
330%2F360+=+x%2F%282%2Api%2A5%29
which simplifies to:
11%2F12+=+x%2F10pi
Cross multiplying we get:
110pi+=+12x
Dividing by 12 we get:
110pi%2F12+=+x
All that's left is to replace pi with a decimal (3.14158....) and simplify the fraction. I'll leave that up to you.