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Illustrator’s Smart Guides system doesn’t detect tangential and perpendicular relations, and Dimension Tool relies on this system.
There is a separate feature request on this you can upvote: Tangent Constraint or Advanced snapping system — http://illustrator.uservoice.com/forums/333657/suggestions/34733398
In scenarios like this I personally rely on a custom plugin from Astute Graphics suite, Perpendicular Line Tool, like one of two GIFs shows. Works for curves as well.
Another method that doesn’t require a plugin would be just to build a perpendicular manually, like the second GIF shows. Will works with straight lines only.