In triangle abc a is a right angle and m b=45 what is the length of bc

We know that angle A is 90 degrees, and angle B is 45 degrees, which means angle C is also 45 degrees. That tells us that BA and CA are equal in length.

a^2 + b^2 = c^2
16^2 + 16^2 = c^2
512 = c^2
sqrt(512) = c
c = 16 sqrt(2)

The answer is B