Final answer:
The area of the triangular-shaped park is calculated using the formula for the area of a triangle with two given sides and the included angle, converted to square yards by dividing the result in square feet by 9.
Step-by-step explanation:
To calculate the area of a triangular-shaped park, we can use the formula for the area of a triangle given two sides and the included angle. In this case, the formula is:
Area = (1/2) × a × b × sin(C)
where ‘a’ and ‘b’ are the lengths of the two adjacent sides, and ‘C’ is the included angle. Given that the lengths are 581 feet and 540 feet, and the angle is 83°, we have:
Area in feet = (1/2) × 581 × 540 × sin(83°)
After calculating the area in square feet, remember to convert it to square yards by dividing by 9, since there are 9 square feet in a square yard:
Area in yards = Area in feet / 9
Plugging the numbers into a calculator will give the area in square yards, and you would then round to the nearest unit to find the correct answer choice.