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The phrase "allowed him to determine" is correct and usable in written English.
It can be used when discussing granting someone the authority or ability to make a decision or judgment about something.
Example: "The new policy allowed him to determine the best course of action for the project."
Alternatives: "permitted him to decide" or "enabled him to assess".
Exact(6)
This allowed him to determine which species of fungi were connecting which plants, and thereby to make an unprecedentedly detailed map of the jungle's social network.
He used a clinometer, a device that allowed him to determine the height by triangulating, using the tree, his own position and the angle of the distance between them.
December 28 , 1798Dundee, Scotland November 23, 1844 Edinburgh, Scotland Thomas Henderson, (born Dec. 28, 1798, Dundee, Angus, Scot. died Nov. 23, 1844, Edinburgh), Scottish astronomer who, as royal astronomer at the Cape of Good Hope (1831 33), made measurements that later allowed him to determine the parallax of a star (Alpha Centauri).
The agent obtained a thermal imaging device that allowed him to determine unusual heat levels in the building.
This stain also allowed him to determine that glial fibres were actually cellular extensions (but not interstitial mass as per Virchow) forming an elaborate three-dimensional intercellular (astrocytic) network that interacts with vascular endothelium.
He therefore set R0 to this value for all oxidation states, and for each oxidation state he took the distances (averaged if necessary) of bonds of known valence as a second fixed point, which allowed him to determine values of b which he found increased monotonically from 0.26 Å for Mn7+ to 0.40 Å for Mn2+.
Similar(54)
The perch allows him to determine which government agencies and programs are financed each year -- and which ones are not.
The fused bone, with the fully erupted wisdom teeth, allow him to determine whether a patient is under or over 18, he said, to within three months.
Taber says his experimental methods will allow him to determine whether positions on race and race-related issues can be "primed" by exposure to subliminal race-related cues.
We consider that the last verdict about what is a threat for the system must be given by a human analyst, whose creative thinking and knowledge about the network allow him to determine the consequences of events marked as malicious by the system.
Using the 100-inch Hooker Telescope at Mount Wilson Observatory in California, he observed Cepheid variable stars in M31 during a search for novae, allowing him to determine their distance by using the stars as standard candles.
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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