
hoch
high / tall
Describes a large vertical extent; the opposite of low.
Der Mount Everest ist der höchste Berg der Welt.
Mount Everest is the highest mountain in the world.
high
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high / tall
Describes a large vertical extent; the opposite of low.
Der Mount Everest ist der höchste Berg der Welt.
Mount Everest is the highest mountain in the world.

high
Describes a large amount, a high level, or a large value.
Die Preise für Benzin sind im Moment sehr hoch.
Gas prices are very high at the moment.

high-ranking
Refers to an important or high-ranking position in a social or professional hierarchy.
Sie hat eine hohe Position im Unternehmen.
She has a high-ranking position in the company.

high-pitched
Describes a high frequency in sounds; the opposite of low.
Sie kann sehr hohe Töne singen.
She can sing very high notes.

high / advanced
Describes an advanced or sophisticated state, often in relation to culture, science, or an era.
Das Hochmittelalter war eine Zeit großer kultureller Blüte.
The High Middle Ages were a time of great cultural flourishing.
When 'hoch' (high) comes before a noun and receives an ending, the word stem changes: the 'c' is dropped. 'hoch' then becomes 'hoh-'. This is an important and fixed rule.
Das ist ein sehr hohes Gebäude.
That is a very tall building.
The adjective 'hoch' (high) is the basis for the noun 'die Höhe' (height) and the verb 'erhöhen' (to increase). If you learn these words together, you can remember the meaning more easily.
Die Höhe des Turms beträgt über 200 Meter.
The height of the tower is over 200 meters.
Very often, 'hoch' (high) describes not only physical height, but also a large amount or high intensity in abstract things. Typical combinations are a high price, high quality, a high risk, or a high fever.
Die Nachfrage nach diesem Produkt ist sehr hoch.
Demand for this product is very high.
In social or professional contexts, 'hoch' (high) describes an important position or important status. For example, people speak of 'eine hohe Position' (a high-ranking position) or 'ein hohes Tier' (literally: a high animal; colloquial for an important person).
Er hat einen hohen Rang beim Militär.
He has a high rank in the military.
In music or speech, 'hoch' (high) describes a high frequency. Typical combinations are 'eine hohe Stimme' (a high voice) or 'ein hoher Ton' (a high note/sound).
Das Baby macht ganz hohe Geräusche.
The baby is making very high-pitched noises.
big / great
Groß and hoch can both describe above-average vertical extent. For people, you usually say how groß they are; for buildings, mountains, and similar things, hoch describes their height. Groß or hoch is therefore more suitable depending on the object, although their meanings partly overlap.

Der neue Turm ist 30 Meter hoch.
The new tower is 30 meters high.
Meine Schwester ist schon 1,80 Meter groß.
My sister is already 1.80 meters tall.