Answer
Central angle of the sector, $\theta$ = 0.5 rad
Work Step by Step
Given-
radius, r = 80 mi
A =1600 $mi^{2}$
Central angle of the sector. $\theta$ = ?
We know that area 'A' of a circular sector with central angle $\theta$ rad and radius 'r' is given by-
A = $\frac{1}{2} r^{2} \theta$
or
1600 = $\frac{1}{2}\times 80^{2}\times \theta$
or
$1600\times2$ = $80^{2}\times \theta$
or
$ \theta$ = $\frac{1600\times2}{80\times80}$ = $\frac{1}{2}$ = 0.5 rad
Therefore, central angle of the sector, $\theta$= 0.5 rad
