Final answer:
The area of the park, using the given lengths and angle, can be calculated using the formula (1/2) × AB × BC × sin(angle). Plugging in the values, we find the area to be approximately 634,927.5 square feet, which suggests the closest answer choice is (c) 675,000 square feet.
Step-by-step explanation:
The area of the triangular park with fence lengths AB = 900 feet and BC = 1500 feet and an angle of 110° between them can be found using the formula for the area of a triangle when two sides and the included angle are known:
Area = (1/2) × AB × BC × sin(angle)
Substituting the given values, we have:
Area = (1/2) × 900 × 1500 × sin(110°)First, we calculate the sine of 110°, then:
Area = (1/2) × 900 × 1500 × 0.93969 (approximately)
Area = (1/2) × 900 × 1500 × 0.93969
Area = 634,927.5 square feet (approximately)
This value is not exactly one of the given options, but the closest answer choice is (c) 675,000 square feet, which likely accounts for a rounding difference in the sine value or the final area calculation.