Answer:
11.2 miles
Explanation:
The mnemonic SOH CAH TOA reminds you that ...
Tan = Opposite/Adjacent
The side you are given is adjacent to the given angle, and the side you are asked to find is opposite the given angle. You can fill in the given values and solve for the required measure.
tan(66°) = BC/(5 mi)
Multiplying by 5 mi gives ...
BC = (5 mi)·tan(66°) = (5 mi)·2.246 = 11.23 mi ≈ 11.2 mi