The angle is 34.4°.
The radius of a circle and the central angle determine the length of an arc. We are aware that the arc length is equivalent to the circumference for an angle of 360 degrees (2π). As the proportion between angle and arc length is constant, we can say that:
L / θ = C / 2π
As circumference C = 2πr,
L / θ = 2πr / 2π
L / θ = r
We find out the arc length formula when multiplying this equation by θ:
L = r * θ
The arc length is equal to the radius multiplied by the central angle.
Radius of the circle, r = 2.70m
Length of the arc, L = 1.60 m
L = rθ
θ = L / r
= 1.60 / 2.70
= 0.6 rad
θ = (0.6 rad × 180° ) / π rad
= 34.4°
Therefore, the angle is 34.4°.
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