Can segments with lengths of 36, 48, and 60 form a triangle? If so, would the triangle be acute, right, or obtuse?

Yes, because by the triangle inequality, a triangle can be formed from three segments of which the sum of the lengths of the two shorter ones exceed the longest segment.

Here we have 36+48=84 > 60, so the three segments form a triangle.

Since the ratio of the sides are 36 : 48 : 60 form the ratio of 3:4:5, which is exactly the ratio of a right triangle, we conclude that the triangle is a right triangle.