A park in a subdivision is triangular shaped. Two adjacent sides of the park are 503 feet and 516 feet. The angle between the sides is 38°. To the nearest unit, what is the area of the park in square yards?

Question

(1 point)
Responses

17,755 square yards
17,755 square yards

26,632 square yards
26,632 square yards

8,877 square yards
8,877 square yards

11,363 square yards

Answer 1

We can use the formula for finding the area of a triangle given two sides and the included angle:

Area = 0.5 * side1 * side2 * sin(angle)

Plugging in the values:

Area = 0.5 * 503 * 516 * sin(38°)
Area = 0.5 * 503 * 516 * 0.6157
Area = 159,904.04 square feet

To convert square feet to square yards, we divide by 9:

Area = 159,904.04 / 9
Area ≈ 17,766 square yards

Therefore, the area of the park to the nearest unit is approximately 17,766 square yards. The closest option is 17,755 square yards.