Answer:
AB = BC = 2√2
Explanation:
Start by focusing on the 45 degree angle. The unknown AB is the side adjacent to this 45 degree angle, and the hypotenuse is known to be 4.
Thus,
cos 45 degrees = adj / hyp = AB / 4, or
AB = 4 cos 45 degrees = 4 (1 / √2) =
4 √2
----------- * --------- = 2√2
√2 √2
Since this is a 45-45-90 triangle, the two shorter sides are equal, and so BC = 2√2 also.