Answer:
$1070.16
Explanation:
You want the prorated amount of taxes if the annual amount is $1743.25 and the sale closes August 12, based on a 360 day year.
Months and days
A 360-day year assumes months are 30 days. The tax charged to the seller will be that for 7 months plus 11 days:
(7·30 +11)/360 × $1743.25 = $1070.16
The seller will pay $1070.16 of the tax bill.
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Additional comment
We have presumed the buyer pays the taxes for August 12, the first day they own the property.