Atrain is chugging up a hill that has a 27 percent grade, which means that for every 100 meters it covers horizontally, it rises 27 meters. what is the angle of inclination?

If you sketch the picture for yourself, you'll see that the 27% ... or 0.27 ... is the tangent of the angle between the horizontal and the slope. With your calculator, you can find the angle whose tangent is 0.27 . It's about 15.1 degrees.