You are asking the same question as in this thread, but now with an illustration of what you want. Again, there is no such thing as the “height” of a triangle. What you are asking for is called “extrusion”. You will get more (and possibly better) answers if you use the proper terminology.

For a sphere mesh you can place the sphere at (0,0,0), then scale the x,y,z components of each of the triangle’s vertices by the same factor > 1.0.

For a generic (non-spherical) mesh, you’d need to apply some additional logic to derive the direction of the extrude.

If you also want the side faces to show, you will have to insert those by yourself by connecting the original triangle vertices with the scaled vertices in a suitable manner.