find the measure of the central angle, where the pendulum of length 40cm travels an arc of 5cm as it swings through an angle
Since s = rθ,
5 = 40θ
To find the measure of the central angle, we can use the formula for the arc length of a circle. The formula is given as:
Arc Length = (angle in radians) * (radius)
In this case, the arc length is given as 5cm, and the radius is the length of the pendulum, which is 40cm. We need to find the angle in radians.
Rearranging the formula, we have:
Angle in radians = Arc Length / Radius
Substituting the given values, we get:
Angle in radians = 5cm / 40cm = 0.125 radians
To convert this angle in radians to degrees, we use the conversion factor:
1 radian = 180 degrees / π
Angle in degrees = (Angle in radians) * (180 degrees / π)
Substituting the value of the angle in radians, we get:
Angle in degrees = 0.125 radians * (180 degrees / π)
Calculating this expression, we find:
Angle in degrees ≈ 7.18 degrees
Therefore, the measure of the central angle is approximately 7.18 degrees.