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

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Question 192554: Given a circle with the radius of 2, which is the length of an arc measuring 75 degrees?
Found 2 solutions by nerdybill, solver91311:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Given a circle with the radius of 2, which is the length of an arc measuring 75 degrees?
.
Circumference = 2(pi)r = 2(3.14)(2) = 12.56
.
Since the entire circle is 360 degrees:
the arc is then
(75/360)(12.56)= 2.62

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The length of the arc of a circle is simply the radius times the measure of the central angle in radians.

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



and then solve for .

But there is a much easier way.



And we know that 45° = and 30° = , so 75° must equal


Then, multiplied by the radius, 2, your arc length is

John