If a circle has a radius of 8 cm. what is the length, in centimeters, of the arc that is intercepted by a central angle of 60 degrees?
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A central angle is measured by its intercepted arc.
Let's denote the length of the intercepted arc with s, and the length of the radius r. So,
s = 6 cm and r = 30 cm.
When a central angle intercepts an arc whose length measure equals the length measure of the radius of the circle, this central angle has a measure 1 radian.
To find the angle in our problem we use the following relationship:
measure of an angle in radians = (length of the intercepted arc)/(length of the radius)
measure of our angle = s/r = 6/30 = 1/5 radians.
Now, we need to convert this measure angle in radians to degrees.
Since pi radians = 180 degrees, then
1 radians = 180/pi degrees, so:
1/5 radians = (1/5)(180/pi) degrees = 36/pi degrees, or approximate to 11.5 degrees.
did u get it
the list of possible answers given are in terms of pi