高 is a picture of a tall building or watchtower — a structure rising up with a roof on top and a doorway below. It has meant 'tall / high' for over 3,000 years, the shape barely changed.
高 is tall, high, and by extension lofty or superior: 高人 (a person of great skill), 高兴 (happy, 'high spirits'). It's also a common surname (高). 高大 = 'tall and big', 高山 = high mountains (with 山). When something rises — a building, a price, a mood, a status — Chinese reaches for 高.
A tall tower with a roof and a door below — HIGH, TALL.
高兴 ('high spirits') means happy. 高 lifts many words: 高山 (high mountain), 高手 (a master/expert, 'high hand'), 高大 (tall and grand).