Creating Triangles with rounded corners but keep inside angles sharp
Create your triangle first, with the right dimensions, and then go to Effect>Stylize>Round Corners. Easy as pie.
This method is great if you want the inner and outer angles all rounded. But if you want only the points of the triangle rounded, then you'll need to do this:
1. Make a normal star and make a copy of it just to the side of it.
2. With the new copy, apply the 'round corners' effect as described above.
3. Align the two stars (both the rounded and original triangle).
4. Carefully Select the star with rounded corner effect and Choose Object > Expand Appearance.
5. Select both stars (make sure that original triangle is on top) and use the 'Crop' Tool in the pathfinder. It will correct the inside angles, and then all you need to do is carefully select the pointy tips and easily delete them.
This will leave you with rounded tips and keep the sharp angles inside.
You can alter the softness of the tips by using a different corner radius in the "round corners" dialog.
Then