An arc with 3 units length and 4 units radius has the central angle of 0.75 radians.
The length of an arc is proportional to its central angle.
Let:
l = length of an arc
a = magnitude of the arc's central angle
r = radius of the corresponding circle
Then, the following holds:
a/2π = l / C
Where C = circumference of the circle = 2 πr
Hence,
a/2π = l / 2 πr
a = l/r (equation 1)
Parameters given in the problem:
l = 3 units
r = 4 units
Plugs these parameters into equation 1
a = 3/4 = 0.75 radians.
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