Question

Arc length s. Central Angle 36 feet. π/2 radiansFind the radius r of a circle with an arc length s and a central angle 0.

Answer 1

The formula for determining the length of an arc is expressed as

length of arc = #/360 * 2 * pi * radius

where

# represents the central angle

From the information given

length of arc = 36

We would convert from radians to degree

1 pi rad = 180 degrees

pi/2 rad = 180/2 = 90 degrees

Thus, # = 90 degrees

The equation becomes

36 = 90/360 * 2 * pi * radius

36 = 0.25 * 2 * 3.14 * radius

36 = 1.57 * radius

radius = 36/1.57

radius = 22.93 feet