Question: I have a friend (yes it's actually a friend and not me) who lost his password for their Bitcoin-qt wallet and can't access is Bitcoin. The wallet is installed on the hard drive of a MacBook and he doesn't know any of the characters Does anyone know how we can get this coin back without his wallet password?

Answer: 
> 
> As seen from the example image, we actually could not know that transaction-3 is located under that specific block and leaf-node since a light client only downloads the merkle root
> 
> 
> 

As a light client, you would be given the branch/path of the tree which corresponds to the transaction you wish to know about, not just the merkle root. By giving you the transaction itself, and the branch of the tree, it lets you verify that the transaction was indeed part of that merkle root. Otherwise there is no way to tell, it is not possible to extra transaction IDs from a merkle root without being given the tree of transactions themselves. A merkle root is just a hash, a 'summary' and commitment to the transactions, it doesn't actually contain any information.
From a previous [Stack answer](https://bitcoin.stackexchange.com/questions/10479/what-is-the-merkle-root). 

"We start with just our transaction and its sibling (if it has one) and calculate the hash of those two and verify that it matches the expected value. From that we can ask for the sibling branch of that and calculate the hash of that and verify it. And continue with this process, up the tree. Which only takes ten verifications for 868 transactions. (That's one of the great things about trees, they can hold a lot of values with only a relatively small number of layers.)"

So if we start at TX3, we can work our way up the tree to the merkle root and verify that the transaction took place.