It is easier to tell with this diagram 
But what about this one ? For triangle BDC.
Here , how do you tell either BD or DC is base ?
It is easier to tell with this diagram 
But what about this one ? For triangle BDC.
Here , how do you tell either BD or DC is base ?
Any side of a triangle (right or not) can be its base. It is something you choose, so choose whatever is most convenient for your calculation. Once you've chosen a base, the height of the triangle is the distance from the base to the opposite vertex.
For example, to calculate the area of this triangle

We could take
No matter which side we choose as base, the area calculated is the same.