see the picture attached to better understand the problem
we know that
the bridge is 10 ft tall and 27 ft long, horizontally
so
BC=10 ft
DE=27 ft---------> DC=27/2----> 13.5 ft
DA=r (radius of the circle)
AC=r-10
Applying the Pythagoras Theorem
DA²=DC²+AC² ------> r²=13.5²+(r-10)²----> r²=182.25+r²-20r+100
20r=282.25--------> r=14.11 ft
the answer is
r=14.11 ft
