How do you find the radian measure of the central angle of a circle of radius 14.5 centimeters that intercepts an arc of length 25 centimeters?

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Answer 1 · 2018-05-02T16:08:09

Divide the arc length by the radius to get your angular displacement in radians (#theta=1.72414=0.549pi#)

The arc length of a circle, with respect to a given radius and angle, can be written as an equation:

#S=rtheta#

Where #S# is the arc length, #r# is the radius, and #theta# is the angle in radians. Plugging in the values we do know:

#25=14.5theta#

#theta=25/14.5#

#color(green)(theta=1.72414" rad")#

if we need to express it in terms of #pi#, since radians are (essentially) fractions of #pi#:

#color(green)(theta=0.549pi" rad")#