The part of Freytag's pyramid that best fits the rise of King Hrothgar after the previous king's death in "Beowulf" would be the exposition. This is where the setting and characters are introduced, providing the background information necessary for understanding the rest of the story.
Beowulf owes a family debt to Hrothgar because Hrothgar's father helped settle a feud and make peace with Beowulf's father, Ecgtheow. Beowulf's father was indebted to Hrothgar's father for his assistance, which Beowulf sees as a reason to repay the debt by helping Hrothgar against the monster, Grendel.
Once at Hrothgar's throne, Beowulf introduces himself as a hero who can crush water sprites, among other things. Therefore he is equipped to defeat Grendel, if Wyrd (or Fate) will have it so. Hrothgar welcomes Beowulf as the son of Ecgtheow, the man whom Hrothgar had helped in settling a feud with the Wylfingas long ago.
Edgetho and Hrothgar are not friends. In the epic poem "Beowulf," Edgetho is Beowulf's father and Hrothgar is the king of the Danes whom Beowulf helps by defeating the monster Grendel. There is no indication of friendship between Edgetho and Hrothgar in the poem.
Beowulf's father took refuge in Hrothgar's land after a messy murder back at home. He eventually married Hrothgar's daughter, and then came baby Beowulf. So long story short Hrothgar is Beowulf's grandfather.
Beowulf and his men travel to Hrothgar's kingdom to kill Grendel.
Beowulf asks Hrothgar to send his armor to Hygelac if he is unsuccessful in defeating Grendel.
It takes Beowulf and his men five days to reach Hrothgar.
'Beowulf' is the epic story that tells us the tale of hero Beowulf, the strongest and bravest of them all and how he defeats monsters and becomes a king. Among several characters we will also meet Hygelac, his uncle and king of the Geats, the one who opens his kingdom's doors and his heart to Beowulf.
Beowulf introduces himself to Hrothgar by stating his name and lineage, and explaining that he has come from the land of the Geats to offer his help in defeating the monster Grendel. He also recounts his previous exploits and asks for permission to face Grendel alone.
Hrothgar knows of Beowulf through his reputation as a great Geat warrior who has come to offer his services to help rid Heorot of the monster Grendel. Word of Beowulf's previous heroic feats and strength as a warrior has spread far and wide, making him well-known even to Hrothgar.
Hrothgar leaves Beowulf in charge of Heorot because Beowulf successfully defeated Grendel and his mother, ensuring the safety of the hall. Hrothgar trusts Beowulf's leadership capabilities and valor in defending the Danes from further threats.
he promises Beowulf great treasures