Normally with trees you wouldn't need to know the height of the tree in order to traverse it. You'd just write a recursive function like this:
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void traverseTree(Node* root){
doStuff(root); // do something with the current node
if (root->leftchild != NULL){traverseTree(root->leftchild );}
if (root->rightchild != NULL){traverseTree(root->rightchild);}
}