Question

What is the distance BC between the two horizontal parallel bars?

Answer 1

One thing you should notice is that the transverse line and the parallel line form a right triangle. We are told that the base is 4 and the angle between the hypotenuse and the leg is 45°

From this we can solve for the second leg. Here's the list of trig functions

sinФ = opposite/hypotenuse
cosФ = adjacent/hypotenuse
tanФ = opposite/adjacent

Since we are only given the adjacent and we are trying to solve for the opposite leg, we can deduce we use tanФ. So we get

$tan45 = x/4$

Multiply by 4 to isolate x and we get

$4*tan45$ = x
Hopes this helps!