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Discover Ludwig"reach heights" is a correct and usable phrase in written English.
It is often used in the context of achieving success or considerable accomplishments. For example: "The hardworking student was determined to reach great heights in his studies."
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Particles reach heights related to their diffusion coefficients.
Competitors reach heights of more than 25 feet.
He could reach heights few others could aspire to.
Shifting dunes, such as Mount Tom, may reach heights of almost 200 feet (60 metres).
Stalagmites are not so restricted and can reach heights of tens of metres.
These trunks may reach heights of 25 metres (80 feet) or more in some species.
The tree can reach heights over 114 metres (375 feet) and is the tallest angiosperm (flowering plant) species.
At maturity a Ginkgo tree can reach heights of 20 to 30 metres (65 to 100 feet).
Some trees reach heights of 300 feet (90 metres) and diameters of more than 7 feet (2 metres).
Under these conditions, storms can reach heights of 60,000 feet and produce hail in excess of 4 inches.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com