Since the railroad trestle is a straight path connecting the two cliffs, we know that after the train has traveled $ 3/4 $ of the trestle's length, the train has traveled both $ 3/4 $ the horizontal distance between the two cliffs and the $ 3/4 $ of the vertical distance between the cliffs' heights. The difference between the heights of the two cliffs is $ 172-112=60 $ feet. $ 3/4 $ of that difference is $ 45 $ feet. Since the train started from the higher cliff and was moving toward the lower cliff, it has descended $ 45 $ feet from its original altitude of $ 172 $ feet. Therefore, the train is now $ 172-45=\boxed{127} $ feet above the bottom of the gorge.