If a an arc of length 5.5 yards subtends a central angle of 0.5 radians on a circle, then the radius of the circle has length: How many yards?

1 Answer
Mar 14, 2018

radius #r=11 yards#.

Explanation:

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First convert the radians into degrees.
#1 rad=(180/pi)degrees #
#0.5 rad=0.5*(180/pi)degrees=(90/pi)degrees#
#theta/360*2pir=#length of an arc, where, #theta # is the angle subtended by the arc in degrees.
Thus, plugging in the values in the equation,
we get:
#(90/pi)*1/360*2*pi*r=5.5 # yards
Simplify that to get:
#(r/2)=5.5# yards
#r=5.5*2# yards
# =11 yards#

Hope that helps!!