Answer:
Of the options provided, only one sentence uses the word "determined" correctly:
She determined her height by using a tape measure.
The other sentences contain incorrect or confusing uses of the word "determined". Here is the analysis:
They listened carefully while the teacher determined the
assignment.
"Determined" should be "gave" or "assigned" the homework. Determined does not make sense here.
He explained the rules to his friend before they determined
the game.
"Determined" should be "decided on" or "chose" the game. Determined is the wrong word choice.
She determined her sister to try a new sport at school.
"Determined" cannot be used as a verb followed by a direct object ("her sister") in this way. This sentence is grammatically incorrect.
The correct option is:
She determined her height by using a tape measure.
Here, "determined" is used properly as a verb meaning "ascertained" or " figured out" something (her height) by some specified method (using a tape measure).
Explanation: