Question

Find the radius of a circle on which a central angle of 3 pie over 2 radians subtends an arc of 60 ft.

Answer 1

First note that a whole circle measures 360 degrees or 2pi radians. The 3/2pi radians is just 3/4 of 2pi, Thus we can say that the length of arc given (the 60 ft) is just 3/4 of the circumference of the circle.
If 60 is just 3/4 of the whole, then 60/(3/4) = 80 ft is the circumference of the circle.
Recall that the circumference of circle is given by
C = 2*pi*r
where r = radius
Substituting,
80 = 2*pi*r
r = 80/(2*pi)
r = 40/pi = 12.74 ft

hope this helps~ :)

Answer 2

If a central angle theta = 3 pi / 2 then :

Circumference of a circle = 2 * r * pi

Ful circle have 360 ° = 2 pi radians.

Lenght of arc :

L = ( theta / 2 pi ) * 2 * r * pi

L = theta * r = 60

( 3 pi / 2 ) * r = 60 Multiply both sides by 2

3 pi * r = 120 Divide both sides by 3 pi

r = 120 / 3 pi = 40 / pi