There is a building quite some distance from The Towers that fell. Why did it collapse?

I think they blew it up on purpose because it was structurally damaged. I remember seeing that on TV and the news guy said that is why. It was 40 stories high.

Assuming you are talking about the 9/11 attacks on the World Trade Centre, it would seem you are referring to Building 7.

As the following website, dedicated to debunking conspiracy theories, notes, it collapsed due to a variety of factors all due to being hit by the Building 1. It highlights, via photographs, the extensive damage to the building caused by the impact of WTC 1 and the fires. It also debunks the conspiracy theory that the building was "pulled" or purposely destroyed as a cover up. http://www.debunking911.com/pull.htm

The wiki also goes over the event: https://en.wikipedia.org/wiki/7_World_Trade_Center#9.2F11_and_collapse It also links to the various official reports that were conducted. WTC 1 hit WTC 7 causing fires, that spread out of control that ultimately weakened the building and brought it down. As the article notes, and one could read for themselves via the numerous links to the NIST report, there was no evidence of conspiracy.