Here is a definition using recursion.

int leftHeight(const Node* t)
{
  if(t == NULL) return 0;
  else return 1 + leftHeight(t->left);
}

Here is a definition using a loop. This one is simple using a loop because you only need to look one direction in the tree (to the left).

int leftHeight(const Node* t)
{
  const Node* r = t;
  int count = 0;
  while(r != NULL) 
  {
     r = r->left;
     count++;
  }
  return count;
}