Final answer:
Hrothgar's character is best exemplified by his trust in Beowulf, illustrated by the line where he entrusts Beowulf with the hall of the Danes, showing his leadership and recognition of Beowulf's valor.
Step-by-step explanation:
The character of Hrothgar in Beowulf is given depth through his actions and words. Looking at the provided options, the statement that most clearly establishes characterization for Hrothgar is the one where he entrusts the hall of the Danes to Beowulf, demonstrating his trust and respect for the warrior.
"Never before, since I could lift shield-arm,/ have I entrusted the hall of the Danes/ to any other man, except to you now."
This line shows Hrothgar's leadership qualities and high standards when he chooses to hand over responsibility to Beowulf. It also reflects the deep trust and respect Hrothgar has for Beowulf, as well as his desperation in light of Grendel's threat. Hrothgar's willingness to pass on such a critical role to Beowulf underlines his recognition of Beowulf's noble and heroic qualities.