Given that a triangle is right, yes, the lengths of the sides containing the right angle can be used as the "height" and the "base".
In general, of course, the triangle won't be right. In such a case, plot the points so you can see which side you feel would most-usefully be the "base". This will probably be the side opposite an angle from which you can drop a perpendicular and have that perpendicular intersect the side.
Find the slope of the line containing the side you've chosen to be the base. Then find the equation of that line.
Find the perpendicular slope, and then the equation of the perpendicular line passing through the vertex opposite the base. This is the line containing your "height" line.
Now that you have two line equations, you can solve the system of equations to find the point where the "height" line reaches the "base" line.
Use the Distance Formula to find the value for the height. Etc, etc, etc.