Question 18891
consider a circle with radius x

ther is a point on circumfrence s where the ship is 
connect this point to the center of circle o

extend os line to outside of circle to point t 
which is the top of the ship

so we have line ost wher os = x and st = 34f

draw a tangent to the circle passing through t and touching the circle 
at point k so we have tk as the distance of swimmer from the tip of the ship 
which is 2.2 miles = 2.2*5280 feet = 11616 Feet

connect k to center of circle o 

u can see a right triangle okt right angled at k

ko = x 
kt = 11616
to = x + 35

So  ko^2 + kt^2 = to^2
 x^2 + 11616^2 = (x + 35)^2
 x^2 + 11616^2 = x^2 + 35^2 + 70x
 11616^2 = 35^2 + 70x
 11616^2 - 35^2 = 70x
134930231 = 70x
x = 134930231/70
  = 1927574Feet
  = 1927574/5280 miles
  = 365 Miles


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