Answer
The central angle of the sector is equal to 0.4 radians.
Work Step by Step
Formula for the area of a circular sector: $$A = \frac 12 r^2 \theta$$
Solving for the central angle of the sector: $$2A = r^2 \theta$$ $$\frac{2A}{r^2} = \theta$$
r = radius = 25 ft
A = 125 $ft ^2$
$$\frac{2(125 \space ft^2)}{(25 \space ft)^2} = \theta$$ $$\theta = 0.4$$
