SOLUTION: Given a circle with a radius of 2 , which is the length of an arc measuring 75

Algebra ->  Circles -> SOLUTION: Given a circle with a radius of 2 , which is the length of an arc measuring 75      Log On


   

Question 456660: Given a circle with a radius of 2 , which is the length of an arc measuring 75
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

So, convert 75° to radians and multiply by 2. Now you could go through the process of setting up a proportion:

%28pi%29%2F180=theta%2F75} then solve for theta

Or, use a much easier way:

write angle 75+ as a sum 45+%2B+30

And we know that 45degrees+=+%28pi%29%2F4 and 30degrees++=+%28pi%29%2F6, so 75degrees+ must equal %28pi%29%2F4+%2B+%28pi%29%2F6+=+5%28pi%29%2F12


Then, multiplied by the radius, r=2, your arc length is 5%28pi%29%2F6} which is 2.62