I was recently presented with this problem:

I solved this problem by first drawing up the parallelogram, like this:

Then I added a few extra lines, like this:

adding the height h and a point P.

After that I set a condition that and stated that and also the fact that

, which I'm too lazy to prove right now, as I'm still struggling with latex.

After this I used the pythagorean theorem to show that which means that

As an effect, this means that , as clearly is bigger than

Then, I just made myself an inequality.

And then finally

, which I was supposed to show.

My question is if I've done everything right, as the book in which I found the problem solves it with trigonometry, and the section for the problem was a section about trigonometry. If my solution is incorrect I need to know why.