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Related topics:1 at or to a level high above the ground, the floor etc [≠ low]: 
He kicked the ball high into the air, over the heads of the crowd.
above the ground
He kicked the ball high into the air, over the heads of the crowd. high above/into etc Hotel Miramar is situated high above the bay. A ski lift whisks you high into the mountains.
Hotel Miramar is situated high above the bay.A ski lift whisks you high into the mountains.2 at or to a high value, cost, amount etc [≠ low]: If prices shoot up any higher, no-one will be able to afford to live in the area. Tom scored higher than anyone else in the class.
value/cost/amount
If prices shoot up any higher, no-one will be able to afford to live in the area.Tom scored higher than anyone else in the class.4 at or to a high rank or level of achievement, especially within a company [≠ low]: It seems that the higher you rise, the less time you have to actually do your job.
achievement
It seems that the higher you rise, the less time you have to actually do your job.5
(leave somebody/something) high and dry
a) if someone is left high and dry, they are left without any help or without the things that they need
b) if a boat, area etc is left high and dry, it is left on land because the water that surrounded it has gone down : The once-thriving port of Rye was left high and dry as sea levels retreated.
The once-thriving port of Rye was left high and dry as sea levels retreated.6 to try to find someone or something by looking everywhere : We looked high and low for Sandy but couldn't find her.
look/search high and low
We looked high and low for Sandy but couldn't find her.