Solution 1:

The forty-foot drop is correct.

Compare this:

1) He's a 10-year old.

2) He's 10 years old.

In the first example, a 10-year old stands as a noun (notice the article preceding it). In the second example, it's not a noun, therefore no article.

Therefore:

1) It's a 40-foot drop.

2) This drop is 40 feet in height.