Given formula is [tex] r= 0.565 \sqrt{a}[/tex]
which gives approximate distance a light beam from a light house where "a" represents the area (in sqaure miles) that the light beam covers
Using this formula we have to estimate the distance the light beam covers the area 1000 square miles.
so that means a=1000
Now plug this value into above formula
[tex] r= 0.565 \sqrt{a}[/tex]
[tex] r= 0.565 \sqrt{1000}[/tex]
[tex] r= 0.565 *31.6227766017[/tex]
r = 17.86686878
Hence final answer is approx 17.87 miles
