An army of orcs has marched upon King Amit's stronghold, setting up camp a safe distance away (or so they think!). What the orcs don’t know is that the king and his engineers have spent the past decade developing advanced catapulting technology. King Amit has created a map to help him compute the distance from each of his two best catapults to the enemy orc camp (shown below). To what distance should King Amit calibrate catapult B to fire?

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In triangle ABC,
angle A = 96 degrees
angle B = 58 degrees
line AB = 145

Update: The answer is apparently 329, but an explanation why would be nice.