Here's what I did (but there's got to be an easier way):
>Drew the obtuse 3D triangle, with vertices at three different Z values.
>On the World Workplane, drew a 2D triangle right under that.
>Gave this 2D triangle Height, thereby making it a 3D object.
>Used the 3D Boolean Slice Tool on that 2D-to-3D object; using the "Slice by Plane (3 Points)" option; using the 3 points of the first, 3D triangle.
>Set a "Workplane by Facet", selecting the top facet of the now-sliced 2D-to-3D object.
But there's got to be an easier way.