Final answer:
The participial phrase in the sentence 'Riding a horse the sheriff looked as if he has stepped out of a history book' is 'Riding a horse'. It provides additional information about the sheriff's action.
Step-by-step explanation:
The phrase 'Riding a horse' in your sentence is the participial phrase. A participial phrase includes a present participle (an -ing ending verb) or past participle (a verb ending in -ed, -d, -t, -en, or -n), and any modifiers, objects, or complements associated with it. In this case, 'Riding a horse' is a present participle phrase that modifies 'the sheriff' - giving us more information about what the sheriff is doing.
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