The ladder, floor and wall form a straight triangle. The angle between floor and wall is obviously 90, between floor and ladder is 38 (given), so the angle between wall and ladder must be (180-90-38 = 52).
The law of sines says that the side length divided by the sine of the opposite corner is a constant for all three corners.
Let's say the floor length is f.
Then 70/sin(38) = f/sin(52), so f = 70*sin(52)/sin(38) ≈ 89.6.
