Do legends with exhaust abilities still trigger their triggered abilities while exhausted?

Ruling: Yes, triggered abilities on legends will still trigger even if the legend is exhausted. The exhausted state only prevents you from activating abilities that require exhausting as a cost.

Nuances:

• As long as the trigger condition (the part before the comma in the ability text) is met, the trigger will go onto the chain regardless of exhausted state
• This can be relevant for trigger ordering when multiple triggers occur simultaneously
• This can create reaction windows that wouldn't otherwise exist