I have concerns about the solution. Posted in comments.

First, is ADB not the ‘smaller-looking’ triangle instead?

Also, the relationship I see between AD/AB = AB/ BC is (side attached to the 90-degree angle) / hypotenuse. So, I am thinking the ratio for triangle CDB should be DC/ BC instead.

Yes, fixed.

What is the relevance of CDB?

It is not. I just wanted to know if I set it up right.

Put it this way: with two pairs of similar triangles, the relevant angles must match, and sides should be in proportion. So if you say that ABC and ADB are similar, it *must* be the case that AB/AD = BC/DB. Same with any other pair you may choose (such as CDB and CBA - CDB and ABC won’t work)

Unfortunately, I still don’t get it.

What exactly is that you don’t get?

I think I get it now. BDC is the triangle that shares an angle with ABC and not CDB, right?

Both triangles share an angle with ABC. The question is - which one? CDB and CBD may look like the same, but they aren’t when making similarity comparisons.

Alright. Thanks.