A park in a subdivision has a triangular shape. Two adjacent sides of the park are 533 feet and 525 feet. The angle between the sides is 53°. Find the area of the park to the nearest square foot.
To find the area of the park, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, the two sides of the triangle form a right angle, so one of the sides can be considered the base and the other side can be considered the height. We can find the height of the triangle using trigonometry.
Let's consider the side of length 525 feet as the base and the side of length 533 feet as the hypotenuse. The height of the triangle can be found using sine:
height = 525 * sin(53°)
height ≈ 433.55 feet
Now we can calculate the area of the triangle:
Area = (1/2) * 525 * 433.55
Area ≈ 113,416.25 square feet
Therefore, the area of the park is approximately 113,416 square feet.