Question #23e2c

1 Answer
Somebody N.
Jan 16, 2018

#24/3# cm

Explanation:

Arc length is given by:

#rtheta#

So:

#r(3/2)=12#

#r=24/3#

#24/3# cm

Reasoning:

If we take a unit circle and allow a terminal side r to move through an angle #theta# describing an arc on the circumference equal to its own length, then the angle #theta# subtended by the arc is 1 radian, and the length of the arc is #rtheta=1#

Since the length of the arc increases at the same rate as the radius increases this is true whatever the radius.

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