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Answer :
Answer:
2π/3 rad
Step-by-step explanation:
To get theta, we will apply the formula for calculating the length of an arc as shown;
Length of an arc = theta/360 * 2πr
theta is the central angle (required)
r is the radius of the circle
Given r = 9 inches and length of the arc PQ = 6π in
Substituting this given values into the formula to get the central angle theta;
6π = theta/360 * 2πr
Dividing both sides by 2πr
theta/360 = 6π/2πr
theta/360 = 3/r
theta/360 = 3/9
theta/360 = 1/3
cross multiplying;
3*theta = 360
theta = 360/3
theta = 120°
Since 180° = π rad
120° = x
x = 120π/180
x = 2π/3 rad
Hence the measure of the central angle in radians is 2π/3 rad
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