The picture shows a barn door what is the distance bc between two horizontal parallel bars?

We know the lenght of the side adjacent to angle A, AC, and we want to know the opposite side, BC. What trig ratio describes the relationship between opposite and adjacent? The Tangent! 

tan (x) = opp / adj
In this case, tan (45°) = BC / 4
To get BC by itself, multiply both sides by 4
4 * tan (45°) = BC

The answer is D

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Hope this helps you